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Khimchenko Boris Nikolaevich

Publications in Math-Net.Ru

  1. A priori estimates for the solution of the first boundary-value problem for a class of second-order parabolic systems

    Izv. RAN. Ser. Mat., 65:4 (2001),  67–88
  2. On a weak (algebraic) extremum principle for a second-order parabolic system

    Izv. RAN. Ser. Mat., 61:5 (1997),  35–62
  3. Necessary and sufficient conditions for satisfying the weak extremum principle for second-order, elliptic systems

    Sibirsk. Mat. Zh., 37:6 (1996),  1314–1334
  4. On a weak extremum principle for a second-order elliptic system

    Izv. RAN. Ser. Mat., 59:5 (1995),  73–84
  5. One-sided estimates for the solutions of the Cauchy problem for second-order parabolic equations in classes of rapidly growing functions. III

    Differ. Uravn., 30:10 (1994),  1750–1759
  6. One-sided estimates for the solutions of the Cauchy problem for second-order parabolic equations in classes of rapidly growing functions. II

    Differ. Uravn., 30:8 (1994),  1362–1369
  7. One-sided estimates for the solutions of the Cauchy problem for second-order parabolic equations in classes of rapidly growing functions. I

    Differ. Uravn., 30:5 (1994),  838–846
  8. An isotropic uniqueness theorem for the solution to the Cauchy problem for a second-order parabolic equation

    Differ. Uravn., 24:1 (1988),  73–85
  9. On the dissipative effect for second-order parabolic operators

    Sibirsk. Mat. Zh., 29:5 (1988),  131–142
  10. A theorem on the space derivative for a second-order one-dimensional parabolic equation

    Differ. Uravn., 22:10 (1986),  1754–1764
  11. A theorem on the interior derivative for an elliptic-parabolic equation of Kolmogorov type

    Differ. Uravn., 22:8 (1986),  1400–1409
  12. A theorem of Nadirashvili type for a second-order parabolic equation with nonnegative characteristic form

    Sibirsk. Mat. Zh., 27:4 (1986),  52–66
  13. Anisotropic classes of uniqueness of the solution of the Cauchy problem for a second-order parabolic equation. II

    Differ. Uravn., 21:8 (1985),  1399–1407
  14. Anisotropic classes of uniqueness of the solution of the Cauchy problem for a second-order parabolic equation. I

    Differ. Uravn., 21:5 (1985),  832–841
  15. A theorem on the interior derivative for a second-order parabolic equation

    Dokl. Akad. Nauk SSSR, 279:6 (1984),  1311–1314
  16. A theorem on an infinite derivative for a second-order parabolic equation with a nonnegative characteristic form

    Differ. Uravn., 20:12 (1984),  2103–2112
  17. A theorem on one-sided a priori boundary estimation for the solution of a second-order degenerate parabolic equation

    Differ. Uravn., 20:10 (1984),  1744–1753
  18. Theorems on the sign of a derivative for a second-order elliptic-parabolic equation

    Differ. Uravn., 20:4 (1984),  641–652
  19. Local Lipschitz boundary estimates for solutions of second-order parabolic equations with nonnegative characteristic form

    Zh. Vychisl. Mat. Mat. Fiz., 24:2 (1984),  240–253
  20. On an aspect of the uniqueness problem for second-order parabolic equations

    Dokl. Akad. Nauk SSSR, 270:2 (1983),  274–277
  21. A countertheorem of Giraud type for a second-order parabolic equation with nonnegative characteristic form

    Differ. Uravn., 19:10 (1983),  1700–1713
  22. An aspect of the development of the theory of the anisotropic strict extremum principle of A. D. Aleksandrov

    Differ. Uravn., 19:3 (1983),  426–437
  23. An approach to the problem of uniqueness for second-order parabolic equations

    Sibirsk. Mat. Zh., 24:5 (1983),  59–70
  24. On investigations of the anisotropic strict extremum principle for second-order elliptic-parabolic equations

    Sibirsk. Mat. Zh., 24:2 (1983),  26–55
  25. On the anisotropic strict extremum principle for a second order elliptic-parabolic equation

    Dokl. Akad. Nauk SSSR, 258:2 (1981),  288–293
  26. The Tikhonov–Petrovskii problem for second-order parabolic equations

    Sibirsk. Mat. Zh., 22:5 (1981),  78–109
  27. A priori estimates of the solution of a second-order parabolic equation in the neighborhood of the lower cap of the parabolic boundary

    Sibirsk. Mat. Zh., 22:4 (1981),  94–113
  28. The strict extremum principle for a weakly parabolically connected, second-order operator

    Zh. Vychisl. Mat. Mat. Fiz., 21:4 (1981),  907–925
  29. On Tihonov–Täcklind classes of uniqueness for degenerate parabolic equations of second order

    Dokl. Akad. Nauk SSSR, 252:4 (1980),  784–788
  30. An aspect of the development of the theory of the isotropic strict extremum principle of A. D. Aleksandrov

    Differ. Uravn., 16:2 (1980),  280–292
  31. On the strong extremum principle for a D-$(\Pi,\Omega)$-elliptically connected operator of second order

    Mat. Sb. (N.S.), 112(154):1(5) (1980),  24–55
  32. Theorems of Giraud type for second-order parabolic equations admitting of degeneration

    Sibirsk. Mat. Zh., 21:4 (1980),  72–94
  33. On uniqueness of the solution of the Cauchy problem for a second order parabolic equation with nonnegative characteristic form

    Dokl. Akad. Nauk SSSR, 248:2 (1979),  290–294
  34. Investigations on the isotropic strict extremum principle

    Dokl. Akad. Nauk SSSR, 244:6 (1979),  1312–1316
  35. The strict extremum principle for a $D-(\Phi ,\,\Omega )$-elliptically connected second-order operator

    Differ. Uravn., 15:7 (1979),  1307–1317
  36. An isotropic strict extremum principle in a planar domain

    Differ. Uravn., 15:7 (1979),  1296–1306
  37. A strict extremum principle that is isotropic in a plane domain

    Sibirsk. Mat. Zh., 20:2 (1979),  278–292
  38. The local behavior of the solution of a second-order parabolic equation near the lower cap of the parabolic boundary

    Sibirsk. Mat. Zh., 20:1 (1979),  69–94
  39. A strong extremum principle for weakly elliptically connected second-order operators

    Zh. Vychisl. Mat. Mat. Fiz., 19:1 (1979),  129–142
  40. Investigations on the maximum principle

    Dokl. Akad. Nauk SSSR, 240:4 (1978),  774–777
  41. On local estimates near the boundary of solutions of a second order equation with nonnegative characteristic form

    Mat. Sb. (N.S.), 106(148):2(6) (1978),  162–182
  42. On a strong extremum principle for degenerating parabolic equations of second order

    Dokl. Akad. Nauk SSSR, 236:5 (1977),  1060–1063
  43. On a priori boundary estimates for the solutions of second order equations with nonnegative characteristic form

    Dokl. Akad. Nauk SSSR, 232:1 (1977),  16–19
  44. Theorems of Giraud type for second order equations with a weakly degenerate non-negative characteristic part

    Sibirsk. Mat. Zh., 18:1 (1977),  103–121
  45. On local estimates of a solution of a second-order parabolic equation near the lower cap of a parabolic boundary

    Dokl. Akad. Nauk SSSR, 227:3 (1976),  543–546
  46. On theorems of Giraud type for a second-order elliptic operator weakly degenerate near the boundary

    Dokl. Akad. Nauk SSSR, 224:4 (1975),  752–755
  47. The maximum principle and local Lipschitz estimates near the lateral boundary for the solutions of a second order parabolic equation

    Sibirsk. Mat. Zh., 16:6 (1975),  1172–1187
  48. The maximum principle and local regularity (in the Lipschitz sense) of solutions of a second-order parabolic equation near the lateral part of the parabolic boundary

    Dokl. Akad. Nauk SSSR, 219:4 (1974),  785–788
  49. A maximum principle and Lipschitz boundary estimates for the solution of a second order elliptic-parabolic equation

    Sibirsk. Mat. Zh., 15:2 (1974),  343–367
  50. On Lipschitz boundary estimates for a solution of a second-order elliptic-parabolic equation

    Dokl. Akad. Nauk SSSR, 212:3 (1973),  544–547
  51. The analogues of the Giraud theorem for a second order parabolic equation

    Sibirsk. Mat. Zh., 14:1 (1973),  86–110
  52. On applications of the maximum principle to parabolic equations of second order

    Dokl. Akad. Nauk SSSR, 204:3 (1972),  529–532
  53. The maximum principle for a second order elliptic-parabolic equation

    Sibirsk. Mat. Zh., 13:4 (1972),  773–789
  54. On the maximum principle for parabolic equations of second order

    Dokl. Akad. Nauk SSSR, 200:2 (1971),  282–285
  55. On the behavior of solutions of elliptic equations near the boundary of a domain of type $A^{(1)}$

    Dokl. Akad. Nauk SSSR, 193:2 (1970),  304–305
  56. On a theorem of M. V. Keldysh and M. A. Lavrent’ev

    Dokl. Akad. Nauk SSSR, 192:1 (1970),  46–47
  57. The boundedness in a closed region of the gradient of a harmonic funcion

    Uspekhi Mat. Nauk, 25:2(152) (1970),  279–280
  58. The behavior of a superharmonic function near the boundary of a region of type $A^{(1)}$

    Differ. Uravn., 5:10 (1969),  1845–1853

© Steklov Math. Inst. of RAS, 2026