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Kamynin Leonid Ivanovich

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. Necessary and sufficient conditions for satisfying the weak extremum principle for second-order, elliptic systems

    Sibirsk. Mat. Zh., 37:6 (1996),  1314–1334
  3. Unilateral estimates for solutions to the second and third boundary value problems (with oblique derivative) for a strongly dissipative second-order parabolic equation

    Sibirsk. Mat. Zh., 37:5 (1996),  1081–1102
  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. Unilateral estimates for a solution to the first boundary value problem for a strongly dissipative second-order parabolic equation over an unbounded domain

    Sibirsk. Mat. Zh., 35:1 (1994),  105–117
  9. Application of parabolic potentials to boundary value problems in mathematical physics. III

    Differ. Uravn., 27:5 (1991),  836–849
  10. Applications of parabolic potentials to boundary value problems in mathematical physics. II

    Differ. Uravn., 27:4 (1991),  627–641
  11. Applications of parabolic potentials to boundary value problems in mathematical physics. I

    Differ. Uravn., 27:3 (1991),  487–496
  12. Applications of parabolic Pagni potentials to boundary value problems in mathematical physics. II

    Differ. Uravn., 27:2 (1991),  250–263
  13. Applications of parabolic Pagni potentials to boundary value problems in mathematical physics. I

    Differ. Uravn., 26:5 (1990),  829–841
  14. Smoothness of parabolic Pagni potentials. III. Proof of a theorem on the smoothness of a Pagni parabolic potential of a simple layer

    Differ. Uravn., 25:5 (1989),  843–860
  15. Smoothness of parabolic Pagni potentials. II. Proof of theorems on smoothness of direct values of Pagni potentials

    Differ. Uravn., 25:4 (1989),  659–674
  16. Smoothness of parabolic Pagni potentials. I

    Differ. Uravn., 25:3 (1989),  477–490
  17. A theorem on the directional derivative for a uniformly parabolic second-order equation

    Sibirsk. Mat. Zh., 30:1 (1989),  114–122
  18. A theorem on the interior derivative for a second-order uniformly parabolic equation

    Dokl. Akad. Nauk SSSR, 299:2 (1988),  280–283
  19. A theorem on an oblique derivative for second-order parabolic equations that admit weak degeneration. II

    Differ. Uravn., 24:5 (1988),  863–875
  20. A theorem on an oblique derivative for second-order parabolic equations that admit weak degeneration. I

    Differ. Uravn., 24:4 (1988),  650–661
  21. On the existence of solutions of the Cauchy problem and of linear boundary value problems for a second-order parabolic equation in an unbounded domain. II

    Differ. Uravn., 24:3 (1988),  445–455
  22. An isotropic uniqueness theorem for the solution to the Cauchy problem for a second-order parabolic equation

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

    Sibirsk. Mat. Zh., 29:5 (1988),  131–142
  24. On the existence of solutions of the Cauchy problem and of linear boundary value problems for a second-order parabolic equation in an unbounded domain. I

    Differ. Uravn., 23:11 (1987),  1937–1948
  25. A theorem on the space derivative for a second-order one-dimensional parabolic equation

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

    Differ. Uravn., 22:8 (1986),  1400–1409
  27. Uniqueness of the solution of linear boundary value problems for a second-order degenerate parabolic equation in an unbounded domain. II

    Differ. Uravn., 22:2 (1986),  305–315
  28. A theorem of Nadirashvili type for a second-order parabolic equation with nonnegative characteristic form

    Sibirsk. Mat. Zh., 27:4 (1986),  52–66
  29. Uniqueness of the solution of linear boundary value problems for a second-order degenerate parabolic equation in an unbounded domain. I

    Differ. Uravn., 21:11 (1985),  1959–1970
  30. 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
  31. 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
  32. A theorem on the internal derivative for a weakly degenerate second-order elliptic equation

    Mat. Sb. (N.S.), 126(168):3 (1985),  307–326
  33. A theorem on the interior derivative for a second-order parabolic equation

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

    Differ. Uravn., 20:12 (1984),  2103–2112
  35. 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
  36. Theorems on the sign of a derivative for a second-order elliptic-parabolic equation

    Differ. Uravn., 20:4 (1984),  641–652
  37. Uniqueness of the solution of the first boundary value problem in an unbounded domain for a second-order parabolic equation

    Zh. Vychisl. Mat. Mat. Fiz., 24:9 (1984),  1331–1345
  38. 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
  39. On an aspect of the uniqueness problem for second-order parabolic equations

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

    Differ. Uravn., 19:10 (1983),  1700–1713
  41. 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
  42. An approach to the problem of uniqueness for second-order parabolic equations

    Sibirsk. Mat. Zh., 24:5 (1983),  59–70
  43. A linear boundary value problem for a second-order elliptic-parabolic equation

    Sibirsk. Mat. Zh., 24:4 (1983),  38–63
  44. On investigations of the anisotropic strict extremum principle for second-order elliptic-parabolic equations

    Sibirsk. Mat. Zh., 24:2 (1983),  26–55
  45. On the uniqueness of solutions of a linear boundary value problem for a second order elliptic-parabolic equation

    Dokl. Akad. Nauk SSSR, 262:4 (1982),  791–794
  46. On the anisotropic strict extremum principle for a second order elliptic-parabolic equation

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

    Sibirsk. Mat. Zh., 22:5 (1981),  78–109
  48. 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
  49. The strict extremum principle for a weakly parabolically connected, second-order operator

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

    Dokl. Akad. Nauk SSSR, 252:4 (1980),  784–788
  51. 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
  52. 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
  53. Theorems of Giraud type for second-order parabolic equations admitting of degeneration

    Sibirsk. Mat. Zh., 21:4 (1980),  72–94
  54. 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
  55. Investigations on the isotropic strict extremum principle

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

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

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

    Sibirsk. Mat. Zh., 20:2 (1979),  278–292
  59. 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
  60. A strong extremum principle for weakly elliptically connected second-order operators

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

    Dokl. Akad. Nauk SSSR, 240:4 (1978),  774–777
  62. Uniqueness of boundary value problems for a second-order degenerate elliptic equation

    Differ. Uravn., 14:1 (1978),  39–49
  63. 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
  64. On a strong extremum principle for degenerating parabolic equations of second order

    Dokl. Akad. Nauk SSSR, 236:5 (1977),  1060–1063
  65. 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
  66. Theorems of Giraud type for second order equations with a weakly degenerate non-negative characteristic part

    Sibirsk. Mat. Zh., 18:1 (1977),  103–121
  67. 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
  68. The uniqueness of the solution of a boundary value problem with A. A. Samarskii's boundary conditions for a second order parabolic equation

    Zh. Vychisl. Mat. Mat. Fiz., 16:6 (1976),  1480–1488
  69. 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
  70. 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
  71. 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
  72. The solution by the method of potentials of the fundamental boundary value problems for a second order one-dimensional parabolic equation

    Sibirsk. Mat. Zh., 15:4 (1974),  806–834
  73. 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
  74. On Lipschitz boundary estimates for a solution of a second-order elliptic-parabolic equation

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

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

    Dokl. Akad. Nauk SSSR, 204:3 (1972),  529–532
  77. On the Gevrey theory for parabolic potentials. VI

    Differ. Uravn., 8:6 (1972),  1015–1025
  78. Gevrey’s theory for parabolic potentials. V

    Differ. Uravn., 8:3 (1972),  494–509
  79. On the Gevrey theory for parabolic potentials. IV, V

    Differ. Uravn., 8:2 (1972),  318–332
  80. The maximum principle for a second order elliptic-parabolic equation

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

    Dokl. Akad. Nauk SSSR, 200:2 (1971),  282–285
  82. On the Gevrey theory for parabolic potentials. III

    Differ. Uravn., 7:8 (1971),  1473–1489
  83. On the Gevrey theory for parabolic potentials. I, II

    Differ. Uravn., 7:4 (1971),  711–726
  84. On the Gevrey theory for parabolic potentials. I, II

    Differ. Uravn., 7:2 (1971),  312–328
  85. The smoothness of thermal potentials in a Dini–Hölder space

    Sibirsk. Mat. Zh., 11:5 (1970),  1017–1045
  86. Solution of the fourth and fifth boundary value problems for a one-dimensional second-order parabolic equation in a curvilinear region

    Zh. Vychisl. Mat. Mat. Fiz., 9:3 (1969),  558–572
  87. The Ljapunov–Gjunter theorems for special thermal potentials

    Dokl. Akad. Nauk SSSR, 179:3 (1968),  531–533
  88. On the smoothness of thermal potentials. VI. Special thermal potentials $P$ and $Q$ on surfaces of type $Ë^{m+1,\alpha,\alpha/2}_{2m+1,1,(1+\alpha)/2}$ and $Ë^{m+1,1,(1+\alpha)/2}_{2m+3,\alpha,\alpha/2}$

    Differ. Uravn., 4:11 (1968),  2034–2055
  89. On the smoothness of thermal potentials. VI. Special thermal potentials $P$ and $Q$ on surfaces of type $Ë^{m+1,\alpha,\alpha/2}_{2m+1,1,(1+\alpha)/2}$ and $Ë^{m+1,1,(1+\alpha)/2}_{2m+3,\alpha,\alpha/2}$

    Differ. Uravn., 4:10 (1968),  1867–1891
  90. On the smoothness of thermal potentials. V. Thermal potentials $U,$ $V$ and $W$ on surfaces of type $Ë^{m+1,\alpha,\alpha/2}_{2m+1,1,(1+\alpha)/2}$ and $Ë^{m+1,1,(1+\alpha)/2}_{2m+3,\alpha,\alpha/2}$. II

    Differ. Uravn., 4:5 (1968),  881–895
  91. On the smoothness of thermal potentials. V. Thermal potentials $U,\,V$ and $W$ on surfaces of type $Ë^{m+1,\alpha,\alpha/2}_{2m+1,1,(1+\alpha)/2}$ and $Ë^{m+1,1,(1+\alpha)/2}_{2m+3,\alpha,\alpha/2}$

    Differ. Uravn., 4:2 (1968),  347–365
  92. The theory of thermal potentials and its applications

    Mat. Zametki, 4:1 (1968),  113–123
  93. Solution of the fifth boundary value problem for a second order parabolic equation in a non-cylindrical region

    Sibirsk. Mat. Zh., 9:5 (1968),  1153–1166
  94. On the smoothness of thermal potentials. IV

    Differ. Uravn., 3:8 (1967),  1303–1312
  95. Smoothness of thermal potentials. IV. Application of the theory of thermal potentials to the solution of a problem of biophysics on the distribution of concentrations in a living cell

    Differ. Uravn., 3:6 (1967),  948–964
  96. The maximum principle and boundary $\alpha$-estimates of the solution of the first boundary value problem for a parabolic equation in a non-cylindrical region

    Zh. Vychisl. Mat. Mat. Fiz., 7:3 (1967),  551–567
  97. A problem of biophysics

    Dokl. Akad. Nauk SSSR, 169:4 (1966),  761–764
  98. On the smoothness of thermal potentials. III

    Differ. Uravn., 2:11 (1966),  1484–1501
  99. On the smoothness of thermal potentials. III. A special single layer thermal potential $P(x,\,t)$ on surfaces of type $Ë^{0,1,\frac{1+\alpha}2}_{1,\alpha,\alpha/2}$ and $Ë_{1,1,\frac{1+\alpha}2}^{1,\alpha,\alpha/2}$

    Differ. Uravn., 2:10 (1966),  1333–1357
  100. On the smoothness of thermal potentials. II. Thermal potentials on the surface of type $Ë^{1,\alpha,\alpha/2}_{1,1,(1+\alpha)/2}$

    Differ. Uravn., 2:5 (1966),  647–687
  101. Schauder type boundary estimates of the solution of a problem with directional derivative for a parabolic equation in a noncylindrical region

    Sibirsk. Mat. Zh., 7:1 (1966),  83–128
  102. Boundary estimates for the solution of an inclined derivative problem for a parabolic equation in a non-cylindrical domain

    Dokl. Akad. Nauk SSSR, 160:3 (1965),  527–529
  103. Ljapunov theorems for heat potentials

    Dokl. Akad. Nauk SSSR, 160:2 (1965),  271–273
  104. On the smoothness of thermal potentials

    Differ. Uravn., 1:6 (1965),  799–839
  105. The existence of a solution of boundary-value problems for a parabolic equation with discontinuous coefficients

    Izv. Akad. Nauk SSSR Ser. Mat., 28:4 (1964),  721–744
  106. Letter to the editor

    Sibirsk. Mat. Zh., 5:5 (1964),  1207
  107. A boundary value problem in the theory of heat conduction with a nonclassical boundary condition

    Zh. Vychisl. Mat. Mat. Fiz., 4:6 (1964),  1006–1024
  108. Boundary estimates for the solution of the third boundary-value problem for a parabolic equation

    Dokl. Akad. Nauk SSSR, 153:3 (1963),  526–529
  109. On the linear Verigin problem

    Dokl. Akad. Nauk SSSR, 150:6 (1963),  1210–1213
  110. The method of heat potentials for a parabolic equation withf discontinuous coefficients

    Sibirsk. Mat. Zh., 4:5 (1963),  1071–1105
  111. The continuous dependence of the solution of linear boundary-value problems on the boundary for a parabolic equation

    Sibirsk. Mat. Zh., 4:3 (1963),  582–610
  112. On the method of potentials for a parabolic equation with discontinuous coefficients

    Dokl. Akad. Nauk SSSR, 145:6 (1962),  1213–1216
  113. A hydraulics problem

    Dokl. Akad. Nauk SSSR, 143:4 (1962),  779–781
  114. The solution of the first boundary-value problem for a quasi-linear parabolic equation in non-cylindrical regions

    Mat. Sb. (N.S.), 57(99):2 (1962),  241–264
  115. On the existence of a solution of Verigin's problem

    Zh. Vychisl. Mat. Mat. Fiz., 2:5 (1962),  833–858
  116. Dependence upon the boundary of the solution of the mixed problem for a parabolic equation

    Dokl. Akad. Nauk SSSR, 140:6 (1961),  1244–1247
  117. The solution of boundary-value problems for a parabolic equation with discontinuous coefficients

    Dokl. Akad. Nauk SSSR, 139:5 (1961),  1048–1051
  118. The solution of the first boundary problem in the large for a quasilinear parabolic equation

    Dokl. Akad. Nauk SSSR, 137:5 (1961),  1049–1052
  119. The stability of parabolic difference equations

    Dokl. Akad. Nauk SSSR, 136:6 (1961),  1287–1290
  120. The maximum principle for parabolic equations with continuous coefficients

    Sibirsk. Mat. Zh., 2:3 (1961),  384–399
  121. Certain properties of solutions of mixed problems for a parabolic equation with discontinuous coefficients

    Dokl. Akad. Nauk SSSR, 133:5 (1960),  1003–1006
  122. On the applicability of Fourier’s method to the solution of the first boundary value problem for a quasilinear equation

    Dokl. Akad. Nauk SSSR, 130:4 (1960),  738–741
  123. On application of the method of finite differences to the solution of the heat conduction equation. II. Convergence of the finite-difference process for the equation of heat conduction

    Izv. Akad. Nauk SSSR Ser. Mat., 17:3 (1953),  249–268
  124. On applicability of the method of finite differences to the solution of the equation of heat conduction. I. Uniqueness of solution of a system of finite-difference equations

    Izv. Akad. Nauk SSSR Ser. Mat., 17:2 (1953),  163–180

  125. Ïîïðàâêà

    Differ. Uravn., 4:3 (1968),  564

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