Skip to main content
SpringerLink
Log in

Olga Arsenievna Oleinik (on her 70th birthday)

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. — “On some mathematical problems of elasticity,”Convegno celebrativo del Centenatio della nascita di Mauro Picone e di Leonida Tonelli, Accad. Naz. dei Lincei, Roma, Atti dei convegni Lincei,77, 259–273 (1986).

    Google Scholar 

  2. — “Some homogenization problems in mechanics of composite materials and porous media,” inMechanics of Nonhomogeneous Structures [in Russian], Naukova Dumka, Kiev (1986), pp. 185–190 (jointly with A. S. Shamaev).

    Google Scholar 

  3. — “Homogenization of the first boundary-value problem and the eigenvalue problem for the elasticity theory system with discontinuous periodic rapidly oscillating coefficients in a perforated domain,”Trudy Tbilissk. Univ., Mat., Mekh., Astron.,19–20, 77–92 (1986) (jointly with G. A. Yosifian and A. S. Shamaev).

    Google Scholar 

  4. -O. A. Oleinik's, “Estimates near the boundary for second-order derivatives of solutions of the Dirichlet problem for the biharmonic equation”Rend. Acad. Naz. Lincei, Ser. 8,80, fasc. 7–12, 525–529 (1986) (jointly with V. A. Kondratiev).

  5. O. A. Oleinik's, “On the estimates for second-order derivatives of the solution of the Dirichlet problem for the biharmonic equation in neighborhoods of corner points of the boundary,”Usp. Mat. Nauk,42, No. 2, 231–232 (1987). (jointly with V. A. Kondratiev).

    Google Scholar 

  6. — “On the spectra of some singularly perturbed operators,”Usp. Mat. Nauk,42, No. 3, 221–222 (1987).

    Google Scholar 

  7. -O. A. Oleinik's, “The uniqueness theorem for classical boundary-value problems of the elasticity theory in unbounded domains,”Usp. mat. Nauk,42, No. 4, 145–146 (1987) (jointly with V. A. Kondratiev).

  8. — “On the behavior at infinity of solutions of elliptic systems with finite energy integral,”Arch. Rat. Mech. Analysis,99, No. 1, 79–89 (1987) (jointly with V. A. Kondratiev).

    Google Scholar 

  9. — “Asymptotic expansions and boundary layers in homogenization problems for differential operators,” in:BALL IV, Proceedings of the Fourth International Conference on Boundary and Interior Layers, Boole Press, Dublin (1987), pp. 145–156.

    Google Scholar 

  10. O. A. Oleinik's “Homogenization problems in elasticity. Spectrum of singularly perturbed operators,” in:Non-classical Continuum mechanics. Lecture Note Series,122, Cambrige University Press (1987), pp. 53–95.

  11. — “Asymptotic properties of solutions of the elasticity system,” in:Applications of Multiple Scaling in Mechanics, Masson, Paris (1987), pp. 188–205.

    Google Scholar 

  12. — “On the uniqueness of solutions to boundary-value problems in unbounded domains, and on isolated singular points of solutions, for the elasticity theory system and second-order elliptic equations,”Usp. Mat. Nauk,42, No. 4, 189–190 (1987) (jointly with V. A. Kondratiev).

    Google Scholar 

  13. — “Korn's inequalities and theorems on the uniqueness of solutions to boundary-value problems for the elasticity theory system in unbounded domains,”Usp. Mat. Nauk.,42, No. 5, 229–231 (1987) (jointly with V. A. Kondratiev).

    Google Scholar 

  14. — “On the homogenization of solutions to the Neumann problem for a second-order elliptic equation and for the elasticity theory system with rapidly oscillating coefficients in a perforated domain,”Usp. Mat. Nauk,42, No. 6, 195–196 (1987) (jointly with G. A. Yosifian and A. S. Shamaev).

    Google Scholar 

  15. — “On the behaviour at infinity of solutions of second-order elliptic equations,” in:Ordinary and Partial Differential Equations, Pitman Research Notes in Mathematics,157, Pitman, London (1987), pp. 161–175.

    Google Scholar 

  16. O. A. Oleinik's “On Korn's inequalities and the uniqueness of solutions to classical boundary-value problems in unbounded domains for the elasticity theory system,” in:Modern Problems of Mathematical Physics [in Russian], Vol. 2, Tbilisi University Press (1987), pp. 15–44 (jointly with V. A. Kondratiev).

  17. — “On the solvability of the von Karman system with nonhomogenious boundary conditions in nonsmooth domains,”Trudy Seminara imeni I. G. Petrovskogo,13, 197–205 (1988) (jointly with O. John, V. A. Kondratiev, D. M. Lekveishvili, and J. Nečas).

    Google Scholar 

  18. — “Some asymptotic problems of linear elasticity,” in:Material Instabilities in Continuum Mechanics and Related Mathematical Problems, Clarendon Press, Oxford (1988), pp. 343–357.

    Google Scholar 

  19. — “On homogenization problems for stratified media,” in:Asymptotic Methods in Mathematical Physics [in Russian], Naukova Dumka, Kiev (1988), pp. 73–83 (jointly with G. A. Yosifian and A. S. Shamaev).

    Google Scholar 

  20. — “On fundamental frequencies of solids with concentrated masses,” in:Mathematical Physics [in Russian], Naukova Dumka, Kiev (1988), pp. 165–171.

    Google Scholar 

  21. — “On free vibration of solids with concentrated masses,” in:Modern Problems of Applied Mathematics and Mathematical Physics [in Russian], Nauka, Moscow (1988), pp. 101–128.

    Google Scholar 

  22. — “On free vibration of a string with a concentrated mass,”Sib. Mat. Zh.,22, No. 5, 71–91 (1988) (jointly with Yu. D. Golovatyi, S. A. Nazarov, and T. S. Soboleva).

    Google Scholar 

  23. O. A. Oleinik's “On free vibration of a homogeneous string with a finite number of concentrated masses,”Usp. Mat Nauk,43, No. 4, 187–188 (jointly with T. S. Soboleva).

  24. — “Boundary-value problems for the elasticity theory system in unbounded domains,”Usp. Mat. Nauk,43, No. 5, 55–98 (1988) (jointly with V. A. Kondratiev).

    Google Scholar 

  25. — “The asymptotics of eigenvalues and eigenfunctions of vibration problems for a medium with singularly perturbed density,”Usp. Mat. Nauk,43, No. 5, 188–190 (1988) (jointly with Yu. D. Golovatyi and S. A. Nazarov).

    Google Scholar 

  26. — “On homogenization of stratified structures,” in:Analyse Matematique et Applications, Gauthier-Villars, Paris (1988), pp. 401–419 (jointly with G. A. Yosifian and A. S. Shamaev).

    Google Scholar 

  27. — “On boundary-value problems for the elasticity theory system,”Usp. Mat. Nauk.,43, No. 4, 180–181 (1988) (jointly with V. A. Kondratiev).

    Google Scholar 

  28. — “On smoothness of generalized solutions to the Dirichlet problem for the biharmonic equation, the Navier-Stokes system, and the von Karman system in nonsmooth two-dimensional domains,” in:Mathematical Modelling. Modern Problems of Mathematical Physics and Computational Mathematics [in Russian], Nauka, Moscow (1989), pp. 212–226 (jointly with V. A. Kondratiev and J. Kopaček).

    Google Scholar 

  29. — “On some mathematical problems of the elasticity theory,” in:Nonlinear Boundary-Value Poblems, No. 1 [in Russian], Naukova Dumka, Kiev (1989), pp. 78–85.

    Google Scholar 

  30. — “The Neumann problem for second-order elliptic equations with rapidly oscillating periodic coefficients in a perforated domain,” in:Partial Differential Equations and the Calculus of Variations, No. 11,Essays in Honor of Ennio De Giorgi, Birkhäuser, Boston (1989), pp. 879–904 (jointly with G. A. Yosifian and A. S. Shamaev).

    Google Scholar 

  31. — “On Korn's inequalities,”C. R. Acad. Sci. Paris, Sér. I.,308, 483–487 (1989) (jointly with V. A. Kondratiev).

    Google Scholar 

  32. — “On the limit behavior of the spectrum for a sequence of operators defined in different spaces,”Usp. Mat. Nauk,44, No. 3, 157–158 (1989) (jointly with G. A. Yosifian and A. S. Shamaev).

    Google Scholar 

  33. — “Some generalization of Hardy's and Korn's inequalities and their applications,”Usp. Mat. Nauk,44, No. 4, 205–206 (1989) (jointly with V. A. Kondratiev).

    Google Scholar 

  34. — “On Korn's inequalities for frame-type structures and junctions,”C. R. Acad. Sci. Paris, Sér. I,309, 591–596 (1989) (jointly with D. Cioranescu and G. Tronel).

    Google Scholar 

  35. — “On the spectrum of singularly perturbed operarors,” in:Journées “Equations aux Derivées Partiélles,” Saint-Jean de Monts, Sociéte Mathématique de France, École Polytéchnique (1989), pp. XIV1-XVI10.

    Google Scholar 

  36. — “On the dependence of the constants in Korn's inequalities on the parameters characterizing the geometry of the domain,”Usp. Mat. Nauk,44, No. 6, 157–158 (1989) (jointly with V. A. Kondratiev).

    Google Scholar 

  37. — “Asymptotic expansions for the eigenvalues and eigenfunctions of the vibration problems for a medium with concentrated perturbations,”Trudy Matematicheskogo Instituta imeni V. A. Steklova,192, 42–60 (1990) (jointly with Yu. D. Golovatyi and S. A. Nazarov).

    Google Scholar 

  38. O. A. Oleinik'sMathematical Problems of the Theory of Highly Inhomogeneous Elastic Media [in Russian], Moscow University Press (1990) (jointly with G. A. Yosifian and A. S. Shamaev).

  39. — “Korn's type inequalities for a class of unbounded domains and applications to boundary-value problems in elasticity,” in:Elasticity. Mathematical Methods and Applications, Ellis, Horward Limited, West Sussex, England (1990), pp. 211–233 (jointly with V. A. Kondratiev).

    Google Scholar 

  40. — “On the character of the continuity on the boundary of a nonsmooth region for a generalized solution of the Dirichlet problem for the biharmonic equation,”Mat. Sb.,181, No. 4, 564–575 (1990).

    Google Scholar 

  41. — “On Hardy's and Korn's inequalities for a class of unbounded domains and their applications to the elasticity theory,”Dokl. Akad. Nauk SSSR,312, No. 6, 1299–1304 (1990) (jointly with V. A. Kondratiev).

    Google Scholar 

  42. — “On the constants in Korn's inequalities for thin domains,”Usp. Mat. Nauk,45, No. 4, 129–130 (1990) (jointly with V. A. Kondratiev).

    Google Scholar 

  43. — “Hardy's and Korn's inequalities and their applications,”Rend. Mat. Appl., Ser. VII,10, No. 3, 641–666 (1990) (jointly with V. A. Kondratiev).

    MathSciNet  Google Scholar 

  44. — “Spectral properties of operators singularly depending on parameters and applications to mathematical physics,” in:Integral Equations and Inverse Problems, Longman, Harlow (1990), pp. 190–199.

    Google Scholar 

  45. — “Mathematical problems of the elasticity theory, and Korn's inequalities,” in:Sixth National Congress on Theoretic and Applied Mechanics, Vol. 2, Bulgarian Academy of Sciences Press, Sofia (1990), pp. 172–181.

    Google Scholar 

  46. — “On Boussinesq and Cerruti problems in elasticity,”Rend. Sem. Mat. Univ. Torino,48, No. 1, 1–20 (1990).

    Google Scholar 

  47. — “On vibration of a membrane with concentrated masses,”Bull. Sciences Mathématiques, 2 série,115, 1–27 (1991) (jointly with G. A. Yosifian and J. Sanchez Gubert).

    Google Scholar 

  48. — “On Korn's inequalities and their applications,” in:Nonlinear Boundary-Value Problems, No. 3 [in Russian], Naukova Dumka, Kiev (1991), pp. 35–41.

    Google Scholar 

  49. — “A new approach to Boussinesq and Cerruti problems for the elasticity theory system,”Vestn. Mosk. Univ., Mat. Mekh., No. 1, 12–23 (1991) (jointly with V. A. Kondratiev).

    Google Scholar 

  50. — “Korn's type inequalities and applications to elasticity,”Atti dei Convegni Lincei,92 183–209 (1992).

    Google Scholar 

  51. — “Some mathematical problems of elasticity and Korn's inequalities,” in:Partial Differential Equations, Pitman Research Notes in Math., Vol. 273, Longman, Harlow (1992), pp. 163–179.

    Google Scholar 

  52. — “On asymptotic behaviour of solutions of some nonlinear elliptic equations in unbounded domains,” in:Partial Differential Equations and Related Subjects, Pitman Research Notes in Math. Vol. 269, Longman, Harlow (1992), pp. 163–195 (jointly with V. A. Kondratiev).

    Google Scholar 

  53. — “Some results for nonlinear elliptic equations in cylindrical domains,” in:Operator Calculus and Spectral Theory, Birkhäuser, Basel (1992), pp. 185–195 (jointly with V. A. Kondratiev).

    Google Scholar 

  54. — “Nonlinear elliptic boundary-value problems in unbounded domains and the asymptotic behaviour of their solutions,”C. R. Acad. Sci. Paris, Sêrie I,315, 787–792 (1992) (jointly with J. I. Diaz).

    Google Scholar 

  55. — “Boundary-value problems for nonlinear elliptic equations in cylindrical domains,”J. Partial Diff. Equations,6, No. 1, 10–16 (1993) (jointly with V. A. Kondratiev).

    Google Scholar 

  56. — “Stefan-like problems,”Meccanica,28, 129–143 (1993) (jointly with M. Primicerio and E. V. Radkevich).

    Google Scholar 

  57. O. A.Oleinik's “On asymptotics of solutions of nonlinear elliptic equations in a neighbourhood of a conic point of the boundary,” In:Problèmes aux Limites et Equations Intègrales dans des Domaines non Régulièrs, CIRM, Luminy, 3–7 mai 1993, p. 16 (jointly with V. A. Kondratiev).

  58. — “On asymptotics of solutions of a nonlinear elliptic equation in a cylindrical domain,”Mathematical Physics Studies, Vol. 15, Kluwer, Dordrecht (1994), pp. 234–251.

    Google Scholar 

  59. — “On asymptotics of solutions to nonlinear elliptic equations,”Usp. Mat. Nauk,48, No. 4, 184–185 (1993) (jointly with V. A. Kondratiev).

    Google Scholar 

  60. —Homogenization of Differential Operators and Integral Functionals, Springer, Berlin (1994) (jointly with V. V. Zhikov and S. M. Kozlov).

    Google Scholar 

  61. — “On a homogenization problem for Laplace's equation in a partially perforated domain,”Dokl. Akad. Nauk (Rossiisk.) 333, No. 4, 424–427 (1993) (jointly with W. Jäger and A. S. Shamaev).

    Google Scholar 

  62. —Homogenization of Differential Operators [in Russian], Pizmatlit, Moscow (1993) (jointly with V. V. Zhikov and S. M. Kozlov).

    Google Scholar 

  63. —On a Homogenization Problem for the Laplace Operator in a Partially Perforated Domain with the Neumann Condition on Holes, Preprint No. 93-53, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Heidelberg (1993) (jointly with W. Jäger and A. S. Shamaev).

    Google Scholar 

  64. — “On asymptotics of solutions of some nonlinear elliptic equations in a neighbourhood of a conic point of the boundary,” in:Partial Differential Equations and Functional Analysis. In Memory of Pierre Grisvard, Birkhäuser, Basel (1996), pp. 160–173 (jointly with V. A. Kondratiev).

    Google Scholar 

  65. — “Korn's inequalities for frame type structures and junctions with sharp estimates for constants,”Asymptotic Analysis,8, No. 1, 1–14 (1994) (jointly with D. Cioranescu and G. Tronel).

    MathSciNet  Google Scholar 

  66. —Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam (1992) (jointly with G. A. Yosifian and A. S. Shamaev).

    Google Scholar 

  67. — “The scientific work of Gaetano Fichera,” in:Atti del Simposio Internationale, Problemi Attuali dell'Analisi e della Fisica Matematica, Taormina 1992, Università “La Sapienza,” Rome (1993), pp. 7–29.

    Google Scholar 

  68. O. A.Oleinik's Korn's Inequalities for Frame Type Structures and Junctions with Sharp Estimates for the Constants,Publications du Laboratoire d'Analyse Numerique, Université Pierre et Marie Curie, Preprint R 93014 (1993), pp. 1–15 (jointly with D. Cioranescu and G. Tronel).

  69. —Some Asymptotic Problems of the Theory of Partial Differential Equations. Lezioni Lincei, Accademia Nazionale dei Lincei, Cambridge University Press, Cambridge (1995).

    Google Scholar 

  70. — “On boundary-value problems for elliptic equations with rapidly alternating type of boundary conditions,”Usp. Mat. Nauk,48, No. 6, 163–164 (1993) (jointly with G. A. Chechkin).

    Google Scholar 

  71. O. A.Oleinik's “On Asymptotics of Solutions and Eigenvalues of an Elliptic Problem with Rapidly Alternating Type of Boundary Conditions,”International Centre for Theoretical Physics, Trieste, Preprint SMR 719/4 (1993).

  72. — “On homogenization of solutions to a boundary-value problem for Laplace's equation in a partially perforated domain with Dirichlet conditions on the holes,”Dokl. Akad. Nauk (Rossiisk.),337, No. 2, 168–171 (1994) (jointly with A. S. Shamaev).

    Google Scholar 

  73. — “On Korn's inequalities for frame-type structures and junctions with sharp estimates for the constants,”Usp. Mat. Nauk,49, No. 4, 139 (1994) (jointly with G. Tronel and D. Cioranescu).

    Google Scholar 

  74. — “On boundary-value problems for the elasticity theory system with rapidly alternating type of boundary conditions,”Usp. Mat. Nauk,49, No. 4, 114 (1994) (jointly with G. A. Chechkin).

    Google Scholar 

  75. — “On homogenization of boundary-value problems in partially perforated domains,”Usp. Mat. Nauk,49, No. 4, 101 (1994) (jointly with A. S. Shamaev).

    Google Scholar 

  76. — “On some nonlinear elliptic problems of the homogenization theory,”Dokl. Akad. Nauk (Rossiisk.),338, No. 3, 310–312 (1994) (jointly with G. A. Yosifian and R. Temam).

    Google Scholar 

  77. — “On a method of constructing approximations in a homogenization problem for a partially perforated domain,”Differents. Uravn.,30, No. 11, 1994–1999 (1994) (jointly with T. A. Shaposhnikova).

    Google Scholar 

  78. — “On homogenization of solutions to the Dirichlet problem in a general type perforated domain with non-periodic structure,”Vestn. Mosk. Univ., Mat., Mekh., No. 2, 50–56 (1995) (jointly with T. A. Shaposhnikova).

    Google Scholar 

  79. — “On the behavior at infinity of solutions to a class of nonlinear elliptic equations in a cylindrical domain,”Dokl. Akad. Nauk (Rossiisk.),341, No. 4, 446–449 (1995) (jointly with V. A. Kondratiev).

    Google Scholar 

  80. — “Some nonlinear homogenization problems,”Appl. Anal.,57, No. 1-2, 101–118 (1995) (jointly with G. A. Yosifian and R. Temam).

    MathSciNet  Google Scholar 

  81. — “On a homogenization problem in a partially perforated domain with the mixed-type boundary condition on the boundaries of holes containing a small parameter,”Differents. Uravn.,31, No. 7, 1150–1160 (1995) (jointly with T. A. Shaposhnikova).

    Google Scholar 

  82. — “On an approach to investigating asymptotic properties of solutions to nonlinear elliptic equations in cylindrical domains,”Usp. Mat. Nauk,50, No. 4, 149 (1995) (jointly with V. A. Kondratiev).

    Google Scholar 

  83. — “On homogenization problems in partially perforated domains,”Usp. Mat. Nauk,50, No. 4, 100 (1995) (jointly with T. A. Shaposhnikova).

    Google Scholar 

  84. —Averaging and some problems of probability, Center of Stochastic Processes, Department of Statistics, University of North Carolina, Chapel Hill, North Carolina, Technical Report No. 455 (1995).

    Google Scholar 

  85. — “On the Neumann problem for the Laplace operator in partially perforated domains with small density of cavities,”Rendiconti Lincei: Matematica e Applicazioni, Ser. 9,6, No. 3, 133–142 (1995) (jointly with T. A. Shaposhnikova).

    Google Scholar 

  86. — “On asymptotics of solutions and eigenvalues of a boundary-value problem with rapidly alternating boundary conditions for the system of elasticity,”Rendiconti Lincei: Matematica e Applicazioni, Ser. 9,7, No. 1, 5–15 (1996) (jointly with G. A. Chechkin).

    Google Scholar 

  87. -O. A. Oleinik's “On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundaries,”Rendiconti Lincei: Matematica e Applicazioni, Ser. 9,7, No. 2 (1996) (jointly with T. A. Shaposhnikova).

  88. O. A.Oleinik's “On some homogenization problems in partially perforated domains,” in:Trends in Applications of Mathematics to Mechanics, Pitman Monographs and Surveys in Pure and Applied Mathematics,77 (1995), pp. 267–344.

  89. — “On the homogenization of the biharmonic equation in a domain perforated along manifolds of small dimensions,”Differents. Uravn.,32, No. 6, 830–842 (1996) (jointly with T. A. Shaposhnikova).

    Google Scholar 

  90. -O. A. Oleinik's “On large time asymptotics for solutions of nonlinear evolution equations and systems,”Usp. Mat. Nauk,51, No. 5 (1996) (jointly with V. A. Kondratiev).

  91. — “The role of the theory of differential equations in modern mathematics and its applications,”Sorosovskii Obrazovatel'nyi Zh., No. 4, 114–121 (1996).

    Google Scholar 

  92. O. A. Oleinik's “On the homogenization of the Laplace operator in a domain with a subset containing periodically situated channels with the Neumann condition on their boundaries,”Vestn. Mosk. Univ., Mat., Mekh., No. 5 (1996) (jointly with G. Tronel and T. A. Shaposhnikova).

  93. -O. A. Oleinik's “On free boundary problems arising in probability theory,”Usp. Mat. Nauk,51, No. 6 (1996) (jointly with G. Kallianpur).

Download references

Authors
  1. V. I. Arnold
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. I. Vishik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. S. Kalashnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. P. Maslov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S. M. Nikol'skii
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. S. P. Novikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19. pp. 000-000, 0000

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arnold, V.I., Vishik, M.I., Kalashnikov, A.S. et al. Olga Arsenievna Oleinik (on her 70th birthday). J Math Sci 85, 2249–2259 (1997). https://doi.org/10.1007/BF02355835

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02355835

Search

Navigation