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In Recognition of the Seventy–fifth Birthday of Lawrence E. Payne

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Publications of L.E. Payne

  1. Torsion of composite sections, Iowa State College Journal of Science 23 (1949) 381–395.

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  2. An axially symmetric flows and the method of generalized electrostatics, Quart. Appl. Math. 10 (1952) 197–204.

  3. Capacity, virtual mass, and generalized symmetrization (with A. Weinstein), Pac. J. Math. 2 (1952) 633–641.

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  4. On axially symmetric crack, punch and torsion problems, J. Soc. Indus. Appl. Math. 1 (1953) 53–71.

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  5. On axially symmetric crack and punch problems for a medium with transverse isotropy, Proc. of Cambridge Philosophical Society 50 (1952) 466–473.

  6. Torsion of a shaft with a toroidal cavity (with G. Weiss), J. Appl. Phys. 25 (1954) 1321–1328.

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  7. Note on a paper by Davies and Walters on “The effect of finite width of area on the rate of evaporation into a turbulent atmosphere”, Quart. J. Mech. and Appl. Math. 7 (1954) 283–286.

  8. New bounds in harmonic and biharmonic problems (with H.F. Weinberger), J. Math. and Phys. 33 (1955) 291–307.

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  9. Inequalities for eigenvalues of membranes and plates, J. Rat. Mech. and Analysis 4 (1955) 517–529.

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  10. Sur le deux frequences propres consecutives (with G. Polya and H.F. Weinberger), Compt. Rendus des Seances l'Acad Sci. 241 (1955) 917–919.

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  11. On a class of plane and axially symmetric problems in elasticity, Proc. First Ind. Cong. Theor. Appl. Mech. (1955) 1–8.

  12. Multivalued functions in generalized axially symmetric potential theory, Annali Scoula Norm. Sup. di Pisa 10 (1956) 135–145.

  13. On the ratio of two consecutive eigenvalues (with G. Polya and H.F. Weinberger), J. Math. and Phys. 35 (1956) 289–298.

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  14. New isoperimetric inequalities for eigenvalues and other physical quantities, Comm. on Pure and Applied Math. 9 (1956) 531–542.

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  15. The elastic spindle under concentrated torques applied at the poles, J. Sci. and Engr. Res. 1 (1957) 37–42.

  16. Note on a lemma of Finn and Gilberg (with H. F. Weinberger), Acta. Math. 98 (1957) 297–299.

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  17. Lower bounds for vibration frequencies of elastically supported membranes and plates (with H. F. Weinberger), J. Soc. Ind. Appl. Math. 5 (1957) 171–182.

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  18. Remark on a paper of O.G. Owens (with H.F. Weinberger), Duke Math. Journal, Vol. 24 (1957), 233–234.

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  19. Mean value theorems in the theory of elasticity (with J.B. Diaz), Proc. 3rd U.S. National Congress of Appl. Mech. (1958) 293–303.

  20. New bounds for solutions of second order elliptic partial differential equations (with H.F. Weinberger), Pac. J. Math. 8 (1958) 551–573.

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  21. Inequalities for eigenvalues of supported and free plates, Quart. Appl. Math. 16 (1958) 111–120.

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  22. On a mean value theorem and its converse, for the displacements in the theory of elasticity (with J.B. Diaz), Portug. Math. 17 (1958) 123–126.

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  23. L'effet d'une contrainte rectiligne sur la frequence fundamentale d'une membrane vibrante (with J. Hersch), Comp. Rend. Seances l'Acad. Sci. 249 (1959) 1855–1857.

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  24. Representation formulas for solutions of a class of partial differential equations, J. Math. Phys. 38 (1959) 145–149.

  25. Bounds in the Cauchy problem for the Laplace equation, Archive Rat. Mech. Anal. 5 (1960) 35–45.

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  26. Upper and lower bounds for the center of flexure, J. Research N.B.S. 64B (1960) 105–111.

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  27. An optimal Poincaré inequality for convex domains (with H. F. Weinberger), Archive Rat. Mech. Anal. 5 (1960) 286–292.

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  28. A Faber-Krahn inequality for wedge-like membranes (with H.F. Weinberger), J. Math. Phys. 39 (1960) 182–188.

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  29. A note on inequalities for plate eigenvalues, J. Math. Phys. 39 (1960) 155–159.

  30. The Stokes flow problem for a class of axially symmetric bodies (with W.H. Pell), J. Fluid Mechanics 7 (1960) 529–549.

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  31. The Stokes flow about a spindle (with W.H. Pell), Quart. Appl. Math. 18 (1960) 257–262.

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  32. On Stokes flow about a torus (with W.H. Pell), Mathematika 7 (1960) 78–92.

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  33. Some isoperimetric inequalities for membrane frequencies and torsional rigidity (with H.F. Weinberger), J. Math. Anal. Appl. 2 (1961) 210–216.

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  34. On Korn's inequality (with H.F. Weinberger), Archive Rat. Mech. Anal. 8 (1961) 89–98.

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  35. Pointwise bounds in the Cauchy problem for elastic plates, J. Res. N.B.S. 65 (1961) 157–163.

  36. On the continuation of solutions of the equations of elasticity by reflection (with J.H. Bramble), Duke Math. J. 28 (1961) 247–252

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  37. On some new continuation formulas and uniqueness theorems in the theory of elasticity (with J.H. Bramble), J. Math. Anal. 3 (1961) 1–17.

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  38. An analogue of the spherical harmonics for the equations of elasticity (with J.H. Bramble), J. Math. Phys. 40 (1961) 163–171.

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  39. A priori bounds in the first boundary value problem in elasticity (with J.H. Bramble), J. Research N.B.S. 65 (1961) 269–276.

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  40. A new decomposition formula in the theory of elasticity (with J.H. Bramble), J. Research N.B.S. 654 (1961) 151–156.

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  41. Bounds for derivatives in the Dirichlet problem for Poisson's equation (with J.H. Bramble), J. Soc. Ind. Appl. Math. 10 (1962) 370–380.

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  42. Some uniqueness theorems in the theory of elasticity (with J.H. Bramble), Archive Rat. Mech. Anal. 9 (1962) 319–328.

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  43. On the uniqueness problem in the second boundary value problem in elasticity (with J.H. Bramble), Proc. 4th National Congress Appl. Mech. (1962) 469–474.

  44. Some inequalities for vector functions with applications in elasticity (with J.H. Bramble), Arch. Rat. Mech. Anal. 11 (1962) 16–26.

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  45. Bounds in the Neumann problem for second order uniformly elliptic operators (with J.H. Bramble), Pac. J. Math. 12 (1962) 823–833.

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  46. Some isoperimetric inequalities in the torsion problem for multiple connected domains, Studies Math. Analy. and Related Topics, Stanford University Press (1962) 270–280.

  47. Bounds for solutions of second order elliptic partial differential equations (with J.H. Bramble), Contributions to Differential Equations 1 (1963) 95–127.

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  48. Some integral inequalities for uniformly elliptic operators (with J.H. Bramble), Contributions to Differential Equations 1 (1963) 129–135.

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  49. New mean value theorems in the mathematical theory of elasticity (with J.B. Diaz), Contributions to Differential Equations 1 (1963) 29–38.

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  50. Some mean value theorems in elastostatics (with J.H. Bramble), J. Soc. Ind. and Appl. Math. 12 (1964) 105–114.

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  51. Some converses of mean value theorems in the theory of elasticity (with J.H. Bramble), J. Math. Anal. Appl 10 (1965) 553–567.

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  52. Pointwise bounds in the first biharmonic boundary value problem (with J.H. Bramble), J. Math. Phys. 42 (1963) 278–286.

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  53. Error bounds in the pointwise approximation of solutions of elastic plate problems (with J.H. Bramble), J. Res. N.B.S. 67 (1963) 145–155.

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  54. Inequalities for solutions of mixed boundary value problems for elastic plates (with J.H. Bramble), J. Res. N.B.S. 68B (1964) 75–92.

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  55. Effect of error in measurement of elastic constants on the solutions of problems in classical elasticity (with J.H. Bramble), J. Res. N.B.S. 67 (1963) 157–167.

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  56. Upper and lower bounds in equations of forced vibration type (with J.H. Bramble), Arch. Rat. Mech. Analy. 14 (1963) 153–170.

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  57. Some explicit inequalities for uniformly elliptic operators, Duke Math. Journal 31 (1964) 485–490.

  58. Bounds for solutions of second order elliptic equations in terms of arbitrary vector fields (with H.F. Weinberger), Arch. Rat. Mech. Anal. 20 (1965) 95–106.

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  59. Isoperimetric inequalities for eigenvalues and their applications, Autovalori e Autosoluzioni C.I.M.E. (1962) 1–58.

  60. Bounds for derivatives in elliptic boundary value problems (with J.H. Bramble), Pac. J. Math. 14 (1964) 777–782.

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  61. Uniqueness criteria for steady state solutions of the Navier-Stokes equations. Simpos. Internaz. Appl. Anal. Fis. Mat (Sardinia, 1964), Cremonese, Rome (1965) 130–153.

  62. Some isoperimetric inequalities in the torsion problem for perfectly plastic beams, Tech. Note BN-362, U. of Maryland (1964).

  63. Mean value theorems for polyharmonic functions (with J.H. Bramble), Amer. Math. Monthly 73 (1966) 124–127.

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  64. On some non-well-posed problems for partial differential equations, Num. Sol. of Partial Diff. Eqtns., M.R.C., University of Wisconsin, Wiley Press (1966) 239–263.

  65. On a singular hyperbolic operator (with D. Sather), Duke Math. J. 34 (1967) 147–162.

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  66. On the stability of solutions of the Navier-Sokes equations and convergence to steady state, SIAM J. Appl. Math. 15 (1967) 392–405.

  67. On singular perturbations in non-well-posed problems (with D. Sather), Ann. Mat. Pure Appl. 75 (1967) 219–230.

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  68. On some improperly posed problems for the Chaplygin equation (with D. Sather), J. Math. Anal. Appl. 19 (1967) 67–77.

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  69. Isoperimetric inequalities and their applications, SIAM Review 9 (1967) 453–488.

  70. Bounds for the first derivatives of Green's function (with J.H. Bramble), Rend. Acc. Naz. Lincei 42 (1967) 604–610.

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  71. On some improperly posed Cauchy problems for quasilinear equations of mixed type (with D. Sather), Trans. Amer. Math. Soc. 128 (1967) 135–141.

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  72. Uniqueness in classical elastodynamics (with R.J. Knops), Arch. Rat. Mech. Anal. 27 (1968) 349–355.

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  73. On the stability of solutions of the Navier-Stokes equations backward in time (with R.J. Knops), Arch. Rat. Mech. Anal. 29 (1968) 331–335.

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  74. Stability in linear elasticity (with R.J. Knops), Int. J. Solids Structures 4 (1968) 1233–1242.

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  75. Stability in the traction boundary value problem in linear elasticity (with R.J. Knops), Int. J. Engr. Sci. 6 (1968) 351–357.

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  76. A priori bounds in problems of steady subsonic flows, Inequalities, Academic Press (1967) pp. 241–254.

  77. Error bounds based on a priori inequalities, Numerical Solutions of Partial Diff. Eqns., Academic Press (1966) 83–94.

  78. Extremal principles and isoperimetric inequalities for some mixed problems of Stekloff's type (with J. Hersch), ZAMP 19 (1968) 802–817.

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  79. Bounds for eigenvalues and eigenvectors of symmetric operators (with C. Moler), SIAM J. Num. Anal. 5 (1968) 64–70.

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  80. On an initial-boundary value problem for a class of degenerate elliptic operators (with D. Sather), Ann. Mat. Pura Appl. 78 (1968) 323–338.

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  81. Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. and Math. Special Issue dedicated to B. Sen (1968) 51–59.

  82. Continuous data dependence for the equations of classical elastodynamics (with R.J. Knops), Proc. Camb. Phil. Soc. 66 (1969) 481–491.

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  83. On uniqueness and continuous data dependence in dynamical problems of linear thermoelasticity (with R.J. Knops), Int. J. Solids Structures 6 (1970) 1173–1184.

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  84. On a priori bounds in the Cauchy problem for elliptic equations, SIAM J. Math. Anal. 1 (1970) 82–89.

  85. Some isoperimetric inequalities for harmonic functions, SIAM J. Math. Anal. 1 (1970), 354–359.

  86. One dimensional auxiliary problems and a priori bounds (with J. Hersch), Abh. Math. Sem. Univ. Hamburg 36 (1971) 57–65.

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  87. Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics (with R.J. Knops), Arch. Rat. Mech. Anal. 41 (1971) 363–398.

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  88. Uniqueness theorems in linear elasticity (with R.J. Knops), Springer Tracts in Natural Philosophy #19, Springer-Verlag (1971).

  89. Hölder stability and logarithmic convexity (with R.J. Knops), IUTAM Conference on Instability of Continuous Systems, Herrenalb (1969), Springer (1971) 248–255.

  90. An isoperimetric inequality for the first eigenfunction in the fixed membrane problem (with M. Rayner), ZAMP 23 (1972) 13–15.

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  91. Uniqueness and continuous dependence criteria for the Navier-Stokes equations, Rocky Mount. J. Math. 2 (1971) 641–660.

  92. Some general remarks on improperly posed problems for partial differential equations, Symp. on Non-well-posed Problems and Logarithmic Convexity, Springer Lecture Notes #316 (1973) 1–30.

  93. Nonlinear problems in nuclear reactor analysis (with I. Stakgold), Lecture Notes in Mathematics 322, Springer-Verlag (1972) 298–307.

  94. Some isoperimetric norm bounds for solutions of the Helmholtz equation (with M. Rayner) ZAMP 24 (1973) 105–110.

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  95. On two conjectures in the fixed membrane eigenvalue problem, ZAMP 24 (1973) 721–729.

  96. Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time (with H.A. Levine), J. Diff. Eq. 16 (1974) 319–334.

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  97. Some nonexistence theorems for initial boundary value problems with nonlinear boundary constraints (with H.A. Levine), Proc. Amer. Math. Soc. 46 (1974) 277–284.

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  98. On the mean value of the fundamental mode in the fixed membrane problem (with I. Stakgold), Appl. Anal. 3 (1973) 295–306.

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  99. Nonexistence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elastodynamics (with R.J. Knops and H.A. Levine), Arch. Rat. Mech. Anal. 55 (1974) 52–72.

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  100. Some inequalities for Stekloff eigenvalues (with J. Hersch and M. Schiffer), Arch. Rat. Mech. Anal. 57 (1974) 99–114.

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  101. Some superadditivity results in the torsion problem for multiply connected cross sections (with R. Sperb), J. Elasticity 5 (1975) 141–147.

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  102. Some a priori and isoperimetric inequalities associated with a class of boundary value problems for doubly connected domains (with R. Sperb), SIAM J. Math. Anal. 7 (1976) 451–460.

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  103. On the nonexistence of global solutions to some abstract Cauchy problems of standard and nonstandard types (with H.A. Levine), Rend. di Mat. 8 (1975) 413–428.

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  104. Saddle points and instability of nonlinear hyperbolic equations (with D. Sattinger), Israel J. Math. 22 (1975) 273–303.

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  105. On the nonexistence of entire solutions of nonlinear second order elliptic equations (with H.A. Levine), SIAM J. Math. Anal. 7 (1976) 337–343.

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  106. Improperly posed problems in partial differential equations, CBMS Regional Conference Series in Applied Math 22 (1975) SIAM.

  107. Growth estimates and lower bounds for solutions of equations of nonlinear elastodynamics with indefinite strain energy (with H.A. Levine), J. of Elasticity 5 (1975) 273–285.

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  108. Nonexistence of global weak solutions for classes of nonlinear hyperbolic and parabolic equations (with H.A. Levine), J. Math. Anal. Appl. 55 (1976) 329–334.

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  109. On Hopf type maximum principles for convex domains (with R. Sperb and I. Stakgold), Nonlinear Analysis 1 (1977) 547–559.

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  110. Some remarks on maximum principles, J. D'Analyse Math. 30 (1976) 421–433.

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  111. Some applications of the maximum principle in the problem of torsional creep (with G. Philippin), SIAM J. Appl. Math. 33 (1977) 446–455.

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  112. Some remarks on the problems of elastic torsion and of torsional creep (with G. Philippin), Some Aspects of Mech. of Continua, Sen Memorial Committee (1977) 32–40.

  113. On potential wells and stability in nonlinear elasticity (with R.J. Knops), Math. Proc. Camb. Phil. Soc. 84 (1978) 177–190.

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  114. On some maximum principles involving harmonic functions and their derivatives (with G. Philippin), SIAM J. Math. Anal. 10 (1979) 96–104.

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  115. Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature (with G. Philippin), Nonlinear Analysis 3 (1979) 193–211.

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  116. On the positive spectrum of Schrödinger operators with long range potentials (with G.B. Khosrovshahi and H.A. Levine), Trans. A.M.S. 253 (1979) 211–228.

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  117. On explicit norm inequalities and their applications to partial differential equations, Constructive Approaches to Mathematical Models, Academic Press (1979) 279–292.

  118. Nonexistence of global solutions in nonlinear Cauchy elastodynamics (with R.J. Knops), Arch. Rat. Mech. Anal. 70 (1979) 125–133.

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  119. Uniqueness and continuous dependence of the null solution in the Cauchy problem for a nonlinear elliptic system (with R.J. Knops). In: G. Anger (ed.), Mathematical Research — Inverse and Improperly Posed Problems in Differential Equations, Vol. 1 (1979) 151–160.

  120. On maximum principles for a class of nonlinear second order elliptic equations (with G.A. Philippin), J. Diff. Eqtn. 37 (1980) 39–48.

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  121. Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function, Proc. Royal Soc. Edinburgh 88A (1981) 251–265.

  122. On the convexity of level lines of the fundamental mode in the fixed membrane problem, and the existence of convex solutions in a related free boundary problem (with A. Acker and G.A. Philippin), ZAMP 32 (1981) 683–694.

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  123. On the stabilization of ill posed Cauchy problems in nonlinear elaticity, Contemporary Math. 4 (1981) 1–10.

  124. Some uniqueness and continuous dependence theorems for nonlinear elastodynamics in exterior domains (with R.J. Knops), Appl. Anal. 15 (1983) 33–51.

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  125. A St. Venant principle for nonlinear elasticity (with R.J. Knops), Arch. Rat. Mech. Anal. 81 (1983) 1–12.

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  126. On the numerical solution of the backward heat equation (with J. Bell), Proceedings of the Semester on Computational Methods, Banch Center, Warsaw, Poland, Spring 1980.

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  127. On the cross section of minimum stress concentration in the Saint Venant theory of torsion (with L. Wheeler), J. Elasticity 14 (1984) 15–18.

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  128. On inequalities of Korn, Friedrichs and Babuska-Aziz (with C.O. Horgan), Arch. Rat. Mech. Anal. 82 (1983) 165–179.

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  129. Isoperimetric inequalities in the torsion and clamped membrane problems for convex plane domains (with G. Philippin), SIAM J. Math. Anal. 14 (1983) 1154–1162.

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  130. Spatial decay estimates in transient heat conduction (with C.O. Horgan and L.T. Wheeler), Quart. Appl. Math., 42 (1984) 119–127.

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  131. Decay estimates for second-order quasilinear partial differential equations (with C.O. Horgan), Advances in Appl. Math. 5 (1984) 309–332.

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  132. Decay estimates for a class of second-order quasilinear equations in three dimensions (with C.O. Horgan), Arch. Rat. Mech. Anal. 86 (1984) 279–289.

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  133. Improved stability estimates for classes of ill posed Cauchy problems, Appl. Anal. 19 (1985) 63–74.

  134. Comparison theorems for a class of nonlinear elliptic boundary value problems (with G. Philippin), Nonlinear Anal. 9 (1985) 787–797.

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  135. Continuous dependence on geometry for the backward heat equation (with P.S. Crooke), Math. Methods in Appl. Sci. 6 (1984) 433–448.

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  136. “Best possible” maximum principles, Math. Methods and Models in Mech., Banach Center Pub. 15 (1985) 609–619.

  137. On stability and growth of solutions for classes of initial and boundary value problems, Math. Methods and Models in Mech., Banach Center Pub. 15 (1985) 621–643.

  138. Some applications of “best possible” maximum principles in elliptic boundary value problems, Partial Diff. Eqns. and Dynamical Systems, Pitman Research Notes 101 (1984) 286–313.

  139. Isoperimetric inequalities for polarization and virtual mass (with G.A. Philippin), J. D'Analy. Mat. 47 (1986) 255–267.

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  140. Some isoperimetric inequalities for capacity, polarization, and virtual mass (with G.A. Philippin), Appl. Anal. 23 (1986) 43–61.

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  141. Improved continuous dependence results for a class of evolutionary equations (with K.A. Ames and H.A. Levine). In: H.W. Engl and C.W. Groetsch (eds), Conference on Inverse and Ill Posed Problems, Academic Press (1987) pp. 443–450.

  142. On stabilizing ill posed problems against errors in geometry and modeling. In: H.W. Engl and C.W. Groetsch (eds), Conference on Inverse and Ill Posed Problems, Academic Press (1987) pp. 399–416.

  143. Convection in thawing subsea permafrost (with G.P. Galdi, M.R.E. Proctor and B. Straughan), Proc. Roy. Soc. London 414 (1987) 83–102.

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  144. Unconditional nonlinear stability in penetrative convection (with B. Straughan), Geophys. Astrophys. Fluid Dyn. 39 (1987) 57–63.

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  145. Some remarks on overdetermined systems in linear elasticity, J. Elasticity 19 (1987) 181–189.

  146. Estimates for low frequency elastic scattering by a rigid body (with G. Dassios), J. of Elasticity 20 (1988) 161–180.

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  147. Improved estimates for continuous data dependence in linear elastodynamics (with R.J. Knops), Proc. Camb. Phil. Soc. 103 (1988) 535–559.

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  148. Double diffusion penetrative convection in thawing subsea permafrost (with J.C. Song and B. Straughan), Int. J. Eng. Sci. 26 (1988) 797–809.

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  149. Some comments on the past 50 years of isoperimetric inequalities. In: W.N. Everitt (ed.), Lecture Notes in Pure and Applied Mathematics #129, Marcel Dekker Inc (1991) 143–161.

  150. On geometric and modeling perturbations in partial differential equations. In: R.J. Knops and A.A. Lacey (eds.), L.M.S. Symposium on Non Classical Continuum Mech. Proc., Cambridge Univ. Press (1987) pp. 108–128.

  151. Some special maximum principles with applications to isoperimetric inequalities. In: P.W. Schaefer (ed.), Conference on Maximum Principles and Eigenvalue Problems in Partial Differential Equations, Pitman Research Notes in Math. #175, Longman Publishers (1988) 15–33.

  152. Energy bounds for Rayleigh scattering by an elastic cavity (with G. Dassios), J. Math. Anal. Appl. 138 (1989) 106–128.

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  153. Error estimates for the temperature of a piece of cold ice, given data on only parts of the boundary (with B. Straughan), Nonlinear Analysis 14 (1990) 443–452.

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  154. Analysis of a convective reaction-diffusion equation II (with H.A. Levine, P. Sacks, B. Straughan), SIAM J. Math. Anal. 20 (1989) 133–147.

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  155. Continuous dependence on geometry with applications in continuum mechanics. In: G.A.C. Graham and S.K. Malik (eds), Continuum Mechanics and its Applications, Hemisphere Publ. Co. (1989) 877–890.

  156. Decay estimates for a class of nonlinear boundary value problems in two dimensions (with C.O. Horgan), SIAM J. Math. Anal 20 (1989) 782–788.

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  157. Decay estimates for the constrained elastic cylinder of variable cross section (with J.M. Flavin and R.J. Knops) Quart. Appl. Math. 47 (1989) 325–350.

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  1. University of Virginia, USA

    Cornelius O. Horgan

  2. University of Tennessee, USA

    Philip W. Schaefer

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Horgan, C.O., Schaefer, P.W. & Fosdick, R.L. In Recognition of the Seventy–fifth Birthday of Lawrence E. Payne. Journal of Elasticity 49, 89–99 (1997). https://doi.org/10.1023/A:1007481532685

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