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Vladimir Alexandrovich Kondratiev. July 2, 1935–March 11, 2010

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Selected Papers of V. A. Kondratiev

  1. V. A. Kondratiev, “Elementary derivation of necessary and sufficient conditions for nonoscillation of the solutions of a linear differential equation of second order,” Usp. Mat. Nauk, 12, No. 3, 159-160 (1957).

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  2. V. A. Kondrat’ev, “Sufficient conditions for non-oscillatory or oscillatory nature of solutions of 2nd order equation y″ + p(x)y = 0,” Dokl. Akad. Nauk SSSR, 113, 742–745 (1957).

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  3. V. A. Kondrat’ev, “On the oscillation of solutions of linear differential equations of the third and fourth order,” Dokl. Akad. Nauk SSSR, 118, 22–24 (1958).

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  4. V. A. Kondrat’ev, “The zeros of the solutions of equation y(n) + p(x)y = 0,” Dokl. Akad. Nauk SSSR, 120, 1180–1182 (1958).

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  5. V. A. Kondratiev, “On the oscillation of solutions of linear differential equations of the third and fourth order,” Tr. Mosk. Mat. Obshch., 8, 259–281 (1959).

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  6. V. A. Kondratiev, “Extensions of linear differential operators,” Dokl. Akad. Nauk SSSR, 125, No. 3, 479–481 (1959).

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  7. V. A. Kondratiev, “Oscillatory properties of solution of the equation y″+p(x)y = 0,” Tr. Mosk. Mat. Obshch., 10, 419–436 (1961).

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  8. V. A. Kondratiev, “Bounds for the derivatives of solutions of elliptic equations near the boundary,” Dokl. Akad. Nauk SSSR, 146, No. 1, 22–25 (1962).

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  9. V. A. Kondratiev, “Boundary value problems for parabolic equations in closed regions,” Tr. Mosk. Mat. Obshch., 15, 400–451 (1966).

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  10. V. A. Kondratiev, “The solvability of the first boundary value problem for strongly elliptic equations,” Tr. Mosk. Mat. Obshch., 16, 293–318 (1967).

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  11. V. A. Kondratiev, “Boundary value problems for elliptic equaitons in domains with conical or angular points,” Tr. Mosk. Mat. Obshch., 16, 209–292 (1967).

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  12. Yu. V. Egorov and V. A. Kondratiev, “The oblique derivative problem,” Mat. Sb., 78, 148–176 (1969).

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  13. V. A. Kondratiev, “The smoothness of the solution of the Dirichlet problem for second-order elliptic equations in a piecewise smooth domain,” Differ. Uravn., 6, No. 10, 1831–1843 (1970).

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  14. V. A. Kondratiev, “On summability of positive solutions of differential equations of arbitrary order in a neigborhood of a characteristic manifold,” Mat. Sb., 99, No. 4, 582–593 (1976).

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  15. V. A. Kondratiev, “Singularities of the solution of the Dirichlet problem for a second-order elliptic equation in a neighborhood of an edge,” Differ. Uravn., 13, No. 11, 2026–2032 (1977).

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  16. V. A. Kondratiev, “Solutions of a hyperbolic Cauchy problem in the presence of characteristic points of the initial surface,” Tr. Sem. im. I. G. Petrovskogo, 5, 97–104 (1979).

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  17. O. A. Oleinik, V. A. Kondratiev, and I. Kopachek “On the asymptotic properties of solutions of biharmonic equations,” Differ. Uravn., 17, No. 10, 1886–1899 (1981).

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  18. V. A. Kondratiev, I. Kopachek, and O. A. Oleinik, “The behavior of generalized solutions of second-order elliptic equations and systems of elasticity theory in a neighborhood of a boundary point,” Tr. Sem. im. I. G. Petrovskogo, 2, 135–152 (1982).

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  19. V. A. Kondratiev and O. A. Oleinik, “Estimates for solutions of the Dirichlet problem for the biharmonic equationn in a neighbourhood of an irregular boundary point and in a neighbourhood of infinity. Sent-Venant’s principle,” Proc. Roy. Soc. Edinburgh Sect. A., 93, Nos. 3–4, 327–343 (1982).

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  20. Yu. V. Egorov, V. A. Kondratiev, and O. A. Oleinik, “Sharp estimates in Hölder spaces for generalized solutions of biharmonic equaiton, the system of Navier–Stokes equations and the von Karman system in nonsmooth two-dimensional domains,” Vestn. Mos. Univ., Ser. I Mat Mekh., 6, 22–39 (1983).

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  21. V. A. Kondratiev and O. A. Oleinik, “Boundary value problems for partial differential equaitons in non smooth domains,” Usp. Mat. Nauk, 38, No. 2, 3–76 (1983).

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  22. Yu. V. Egorov and V. A. Kondratiev, “Estimation of smallest eigenvalue for an elliptic operator,” Differ. Uravn., 20, No. 8, 1397–1403 (1984).

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  23. V. A. Kondratiev and O. A. Oleinik, “Time-periodic solutions of a second-order parabolic equation in exterior domains,” Vestn. MGU, Mat.-Mech, 4, 38–47 (1985).

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  24. V. A. Kondratiev, I. Kopachek, and O. A. Oleinik, “Best Hölder exponents for generalized solutions of the Dirichlet problem for a second-order elliptic equaiton,” Mat. Sb., 131, No. 1, 113–125 (1986).

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  25. V. A. Kondratiev, “Estimates near the boundary for second-order derivatives of solutions of the Dirichlet problem for the biharmonic equation,” Atti Acad. Naz. Lincei Rend. Cl. Sci. Fiso. Mat. Natur. (8), 80, Nos. 7–12, 525–529 (1986).

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  26. V. A. Kondratiev and O. A. Oleinik, Asymptotic properties of solutions of elasticity system, Application of multiple scaling in mechanics, Masson, Paris 188–205 (1987).

  27. V. A. Kondratiev and O. A. Oleinik, “Asymptotic behavior in a neighborhood of infinity of solutions with a finite Dirichlet integral of second-order elliptic equations,” Tr. Sem. im. I. G. Petrovskogo, 12, 149–163 (1987).

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  28. Yu. V. Egorov and V. A. Kondratiev, “Estimates for the eigenfunctions of elliptic opeators with constant coefficients,” Tr. Sem. im. I. G. Petrovskogo, 12, 229–237 (1987).

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  29. Yu. V. Egorov and V. A. Kondratiev,“On the estimation of the number of points of the negative spectrum of the Schrödinger operator,” Mat. Sb., 134, No. 4, 556–570 (1987).

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  30. V. A. Kondratiev and O. A. Oleinik, “On the behaviour at infinity of solutions of elliptic system with finite energy integral,” Arch. Ration. Mech. Anal., 99, No. 1, 75–89 (1987).

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  31. E. M. Landis and V. A. Kondratiev, “Qualitative theory of second-order linear partial differential equaitons,” Itogi Nauki i Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napr., 32, 99–215 (1988).

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  32. V. A. Kondratiev and O. A. Oleinik, “Boundary value problems for a system in elastisity theory in unbounded domains. Korn inequalities,” Usp. Mat. Nauk, 43, No. 5, 55–98 (1988).

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  33. E. M. Landis and V. A. Kondratiev, “On qualitative properties of solutions of a second-order nonlinear equaion,” Mat. Sb., 135, No. 3, 346–359 (1988).

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  34. V. A. Kondratiev and E. M. Landis, “Semilinear second-order equaitons with nonnegative characteristic form,” Math. Notes, 44, Nos. 3–4, 728–735 (1989).

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  35. V. A. Kozlov, V. A. Kondratiev, and V. G. Mazya, “On sign veriability and the absence of “strong” zeroes of solutions of elliptic equations,” Izv. Akad. Nauk SSSR., Ser. Mat., 53, No. 2, 328–344 (1989).

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  36. M. I. Vishik, Yu, S, Ilyashenko, A. S. Kalashnikov, V. A. Kondratiev, S. N. Kruzhkov, E. M. Landis, V. M. Millionschikov, O. A. Oleinik, A. F. Filippov, and M. A. Shubin, “Some unsolved problems in the theory of differential equaitons and mathematical physics,” Russ. Math. Surv., 44, No. 4, 157–171 (1989).

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  37. V. A. Kondratiev and E. M. Landis, “The qualitative theory of second-order partial differential equations,” Encycl. Math. Sci., 31, 99–215 (1989).

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  38. Yu. V. Egorov and V. A. Kondratiev, “On negative spectrum of an elliptic operator,” Mat. Sb., 181, No. 2, 147–166 (1990).

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  39. Yu. V. Egorov and V. A. Kondratiev, “The negative spectrum of an elliptic operator,” Tr. Mat. Inst. Steklov., 192, 61–67 (1990).

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  40. V. A. Kondratiev and O. A. Oleinik, “Hardy’s and Korn’s type inequalities and their applications,” Rend. Mat. Appl. (7), 10, No. 3, 641–666 (1990).

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  41. V. A. Kondratiev, I. Kopachek, and O. A. Oleinik, “On character of the continuity of a generalized solution of a Dirichlet problem for a biharmonic equation on the boundary of a nonsmooth domain,” Mat. Sb., 181, No. 4, 564–575 (1990).

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  42. V. A. Kondratiev, “Schauder-type estimates of solutions of second-order elliptic systems in divergence form in non-regular domains,” Commun. Partial Differ. Equ., 16, No. 12, 1857–1878, (1991).

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  43. V. A. Kondratiev and O. A. Oleinik, “A new approach to Bussinesq and Cherruti problems for a system in the theory of elastiity,” Vestn. MGU, Ser. 1, Mat.-Mekh., 1, 12–23 (1991).

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  44. V. A. Kondratiev, “On qualitative properties of solutions of semilinear ellip[tic equations,” Tr. Sem. im. I. G. Petrovskogo, 16, 186–190 (1992).

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  45. V. A. Kondratiev and O. A. Oleinik, “On estimates for the eigenvalues in some elliptic problems,” Oper. Theory Adv. Appl., 57, 51–60 (1992).

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  46. V. A. Kondratiev and O. A. Oleinik, “Some results for nonlinear elliptic equations in cylindrical domains,” Oper. Theory Adv. Appl., 57, 185–195 (1992).

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  47. V. A. Kondratiev and O. A. Oleinik, “On asymptotic behaviour of solutions of some nonlinear elliptic equations in unbounded domains,” Pitman Res. Notes Math. Ser., 269, 169–196 (1992).

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  48. Yu. V. Egorov and V. A. Kondratiev,“ Estimates of the negative spectrum of an elliptic operator,” Am. Math. Soc. Transl. Ser. 2, 150, 111–140 (1992).

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  49. V. A. Kondratiev and O. A. Oleinik, “Boundary value problems for nonlinear elliptic equations in cylindrical domains,” J. Partial Different. Equ., 6, No. 1, 10 –16 (1993).

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  50. V. A. Kondratiev, “Invertibility of Schrödinger operators in weighted spaces,” Russ. J. Math. Phys., 1, No. 4, 465–482 (1993).

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  51. V. A. Kondratiev, “Solutions of weakly nonlinear elliptic equations in a neighborhood of a conic point of the boundary,” Differ. Equ., 29, No. 2, 246–252 (1993).

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  52. V. A. Kondratiev and O. A. Oleinik, “On behaviour of solutions a class of nonlinear elliptic second-order equations in a neighborhood of a conic point of the boundary,” Lect. Not. Pure Appl. Math., 167, 151–161 (1995).

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  53. Yu. V. Egorov and V. A. Kondratiev, “On moments of negative eigenvalues of an elliptic operator,” Math. Nachr., 174, 73–79 (1995).

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  54. V. A. Kondratiev and O. A. Oleinik, “On asymptotics of solutions of nonlinear second-order elliptic equations in cylindrical domains,” Prog. Nonlin. Differ. Equ. Appl., 22, 160–173 (1996).

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  55. Yu. V. Egorov and V. A. Kondratiev, “On estimates for the first eigenvalue in some Sturm–Liouville problems,” Russ. Math. Surv., 51, No. 3, 439–508 (1996).

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  56. Yu. V. Egorov and V. A. Kondratiev, “On spectral theory of elliptic operators” Oper. Theory Adv. App., 89, 1–325 (1996).

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  57. V. A. Kondratiev, “On solutions of nonlinear elliptic equaitons in cylindrical domains,” Fundam. Prikl. Mat., 2, No. 3, 863–874 (1996).

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  58. V. A. Kondratiev, “On some nonlinear boundary value problems in cylindrical domains,” Tr. Sem. im. I. G. Petrovskogo, 19, 235–261 (1996).

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  59. V. A. Kondratiev and F. Nicolosi, “On some properties of the solutions of quasilinear degenerate elliptic equations,” Math. Nachr., 182, 243–260 (1996).

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  60. Yu. V. Egorov and V. A. Kondratiev, “On blow-up solutions for parabolic equations of second order,” Math. Res., 100, 77–84 (1997).

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  61. V. A. Kondratiev and L. Veron, “Asymptotic behaviour of solutions of some nonlinear parabolic or elliptic equations,” Asymptot. Anal., 14, 117–156 (1997).

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  62. Yu. V. Egorov and V. A .Kondratiev, “On a problem of O. A. Oleinik,” Russ, Math. Surv., 6, 1296–1297 (1997).

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  63. V. A. Kondratiev, “On the asymptotic properties of solution of the nonlinear heat equaiton,” Differ. Equ., 34, No. 2, 250–259 (1998).

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  64. Yu. V. Egorov, V. A. Kondratiev, and O. A. Oleinik, “Asymptotic behavior of solutions of nonlinear elliptic and parabolic systems in cylinderical domains,” Mat. Sb., 189, No. 3, 45–68 (1998).

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  65. Yu. V. Egorov and V. A. Kondratiev, “On estimates of the first eigenvalue in some elliptic problems,” Oper. Theory Adv. Appl., 102, 73–84 (1998).

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  66. Yu. V. Egorov and V. A. Kondratiev, “Two theorems on blow-up solutions for semilincar parabolic equations of second order,” C. R. Acad. Sci. Paris, Ser. I Math., 327, No. 1, 47–52 (1998).

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  67. V. A. Kondratiev, “Completeness of root functions of elliptical operators in Banach Spaces,” Russ. J. Math. Phys., 6, No. 2, 194–201 (1999).

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  68. V. A. Kondratiev, “On properties of solutions to nonlinear parabolic equations of the second order,” J. Dyn. Control Syst., 5, 523–546 (1999).

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  69. Yu. V. Egorov and V. A. Kondratiev, “On asymptotic behavior in an infinite cylinder of solutions to an elliptic equation of second order,” Appl. Anal., 71, Nos. 1–4, 25–39 (1999).

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  70. Yu. V. Egorov and V. A. Kondratiev, “On some global existence theorem for a semilinear parabolic problem,” Applied Nonlinear Analysis, Kluwer, N.Y. 67–78 (1999).

  71. V. A. Kondratiev and M. A. Shubin, “Discreteness of the spectrum for Schrödinger operators on a manifold of bounded geometry,” Oper. Theory Adv. Appl., 110 185–226 (1999).

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  72. V. A. Kondratiev amd M. A. Shubin, “Conditions of the discreteness of the spectrum for Schrödinger operators on a manifolds,” Funct. Anal. Appl., 33, No. 3, 231–232 (1999).

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  73. Yu. V. Egorov, V. A. Galaktionov, V. A. Kondratiev, and S. I. Pohozaev, “On the necessary conditions of global existence to a quasilinear inequality in the half-space,” C. R. Acad. Sci. Paris, Ser. I Math., 330, No. 9, 93–98 (2000).

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  74. Yu. V. Egorov and V. A. Kondratiev, “On global solutions to a semilinear elliptic boundary problem in an unbounded domain,” Rend. Instit. Mat. Univ. Trieste, 31, No. 2, 87–102 (2000).

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  75. Yu. V. Egorov and V. A. Kondratiev, “On the behavior of solutions of a nonlinear boundary value problem for a second-order elliptic equaition in an unbounded domain,” Trans. Mosc. Math. Soc., 62, 125–147 (2001).

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  76. Yu. V. Egorov and V. A. Kondratiev, “On the asymptotic behaviour of solutions to a semilinear elliptic boundary problem,” Funct. Differ. Equ., 8, Nos. 1–2, 163–181 (2001).

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  77. V. A. Kondratiev and M. A. Shubin, “Discreteness of spectrum for the magnetic Schrodinger operators,” Commun. Partial Differ. Equ., 27, Nos. 3–4, 477–525 (2002).

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  78. Yu. V. Egorov, V. A. Galaktionov, V. A. Kondratiev, and S. I. Pohozaev, “On the asymptotics of global solutions of higher-order semilinear parabolic equations in the supercritical range,” C. R. Math. Acad. Sci. Paris, 335, No. 10, 805–810 (2002).

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  79. I. Astashova, A. Filinovskii, V. Kondratiev, and L. Muravey, “Some problems in the qualitative theory of differential equations,” J. Nat. Geom., 23, 1–126 (2003).

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  80. V. A. Kondratiev, V. Liskevich, and Z. Sobol, “Second-order semilinear elliptic inequalities in exterior domains,” J. Differ. Equ., 187, 429–455 (2003).

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  81. V. A. Kondratiev, “On the existence of positive solutions of second-order semilinear elliptic equations in cylindrical domains,” Russ. J. Math. Phys., 10, No. 1, 11–20 (2003).

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  82. V. A. Kondratiev, “On the existence of positive solutions of second-order semilinear elliptic equations in unbounded domains,” Funct. Differ. Equ., 10, Nos. 1–2, 283–290 (2003).

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  83. V. Liskevich, V. A. Kondratiev, Z. Sobol, and O. Us, “Estimates of heat Kernels for a class of second-order elliptic operators with applications to semi-linear inequalities in exterior domains,” J. London Math. Soc. (2), 2, No. 69, 107–127 (2004).

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  84. Yu. V. Egorov, V. A. Galaktionov, V. A. Kondratiev, and S. I. Pohozaev, “Global solutions of higher order parabolic semilinear equations,” Adv. Differ. Equ., 9, Nos. 9–10, 1009–1038 (2004).

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  85. V. A. Kondratiev, V. G. Mazya, and M. A. Shubin, “Discreteness and strictly positivity criteria for magnetic Schrödinger Operators,” Commun. Partial Differ. Equ., 29, Nos. 3–4, 39–52 (2004).

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  86. V. A. Kondratiev, V. Liskevich, and V. Moroz, “Positive solutions to superlinear second-order divergence tipe elliptic equations in cone-like domains,” Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 25–43 (2005).

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  87. V. A. Kondratiev, “On positive solutions of weakly nonlinear second-order elliptic equations in cylindrical domains,” Proc. Steklov Inst. Math., No. 3 (250), 169–177 (2005).

  88. V. A. Kondratiev, V. Liskevich, V. Moroz, and Z. Sobol, “A critical phenomenon for sublinear elliptic equations in cone-like domains,” Bull. London Math. Soc., 37, 585–591 (2005).

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  89. M. Borsuk and V. Kondratiev, Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains, Elsevier Science B. V., Amsterdam (2006).

  90. V. A. Kondratiev, “On the asymptotic behavior of weakly nonlinear second-order elliptic equations in a cylindrical domain,” J. Math. Sci., 142, No. 3, 2122–2129 (2007).

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  91. V. A. Kondratiev, “On the asymptotic properties of solutions of nonlinear parabolic equations,” J. Math. Sci., 142, No. 3, 2130–2137 (2007).

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  92. V. A. Kondratiev, “On the asymptotic behavior of weakly nonlinear second-order elliptic equations in a cylindrical domain,” J. Math. Sci., 142, No. 3, 2122–2129 (2007).

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  93. V. A. Kondratiev, “On the asymptotic behavior of solutions of second-order nonlinear elliptic and parabolic equations,” Ukr. Math. Bull., 5, No. 1, 101–116 (2008).

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  94. V. A. Kondratiev, V. A. Liskevich, and Z. Sobol, “Positive solutions to semi-linear and quasilinear elliptic equations on unbounded domains,” Handb. Differ. Equ., 6, 177–267 (2008).

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  95. V. A. Kondratiev, “Positive super-solutions to semi-linear second-order non-divergence type elliptic equations in exterior domains,” Trans. Am. Math. Soc., 361, No. 2, 697–713 (2009).

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  96. V. A. Kondratiev, “The asymptotics of solutions to elliptic equations with nonlinear boundary conditions,” J. Math. Sci., 164, No. 6, 896–905 (2010).

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  97. V. A. Kondratiev, “On positive solutions of the heat equation satisfying a nonlinear boundary condition,” Differ. Equ., 46, No. 8, 1114–1122 (2010).

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 39, Partial Differential Equations, 2011.

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Vladimir Alexandrovich Kondratiev. July 2, 1935–March 11, 2010. J Math Sci 190, 1–7 (2013). https://doi.org/10.1007/s10958-013-1243-7

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