The exterior Dirichlet problem for the biharmonic equation: Solutions with bounded Dirichlet integral

被引：23

作者：

Matevosyan, OA ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2001年 / 70卷 / 3-4期

关键词：

biharmonic equation; exterior Dirichlet problem; Sobolev space; finite-energy solution; Dirichlet integral;

D O I：

10.1023/A:1012347929056

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the unique solvability of the Dirichlet problem for the biharmonic equation in the exterior of a compact set under the assumption that a generalized solution Of this problem has a bounded Dirichlet integral with weight \x \ (a). Depending on the value of the parameter a, we prove uniqueness theorems or present exact formulas for the dimension of the solution space of the Dirichlet problem.

引用

页码：363 / 377

页数：15

共 11 条

[1]

GILLBARG D, 1977, ELLIPTIC PARTIAL DIF

[2]

Kon'kov A.A., 1993, MAT SBORNIK, V184, P23

[3] BOUNDARY-VALUE-PROBLEMS FOR THE SYSTEM OF ELASTICITY THEORY IN UNBOUNDED-DOMAINS - KORNS INEQUALITIES [J].

KONDRATEV, VA ;

OLEINIK, OA .

RUSSIAN MATHEMATICAL SURVEYS, 1988, 43 (05) :65-119

[4]

KONDRATEV VA, 1984, USP MAT NAUK, V39, P165

[5]

Kondratiev V., 1967, T MOSKOV MATEM OBSHC, V16, P209

[6]

KONDRATIEV VA, 1987, ARCH RATION MECH AN, V99, P75, DOI 10.1007/BF00251392

[7]

Kudryavtsev L.D, 1967, IZV AKAD NAUK SSSR M, V31, P354

[8]

Matevosyan O.A, 1998, DIFF URAVN, V34, P806

[9]

MATEVOSYAN OA, 1993, USP MAT NAUK, V48, P159

[10]

Mikhlin SG, 1977, Linear Partial Differential Equations

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