On solutions of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains

被引：15

作者：

Matevossian H.A. ^{[1
,2
]}

机构：

[1] Federal Research Center “Computer Science and Control”, Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Vavilov str. 40, Moscow

[2] Moscow Aviation Institute (National Research University “MAI”), Volokolomskoye shosse 4, Moscow

来源：

p-Adic Numbers, Ultrametric Analysis and Applications | 2017年 / 9卷 / 2期

关键词：

biharmonic equation; mixed Dirichlet-Steklov problem; Sobolev space; weighted Dirichlet integral;

D O I：

10.1134/S2070046617020054

中图分类号：

学科分类号：

摘要：

We study the unique solvability of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains 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 theorem or present exact formulas for the dimension of the solution space of the mixed Dirichlet-Steklov problem in the exterior of a compact set. © 2017, Pleiades Publishing, Ltd.

引用

页码：151 / 157

页数：6

共 38 条

[1] The exterior Dirichlet problem for the biharmonic equation: Solutions with bounded Dirichlet integral
Matevosyan, OA
MATHEMATICAL NOTES, 2001, 70 (3-4) : 363 - 377
[2] The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral
O. A. Matevosyan
Mathematical Notes, 2001, 70 : 363 - 377
[3] Steklov–Farwig Biharmonic Problem in Exterior Domains
G. Migliaccio
H. A. Matevossian
Lobachevskii Journal of Mathematics, 2023, 44 : 2413 - 2428
[4] Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains
Matevossian, Hovik A.
JOURNAL OF SIBERIAN FEDERAL UNIVERSITY-MATHEMATICS & PHYSICS, 2020, 13 (06): : 755 - 762
[5] Steklov-Farwig Biharmonic Problem in Exterior Domains
Migliaccio, G.
Matevossian, H. A.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2023, 44 (06) : 2413 - 2428
[6] On solutions of the mixed Dirichlet-Navier problem for the polyharmonic equation in exterior domains
Matevosyan, O. A.
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2016, 23 (01) : 135 - 138
[7] Steklov Biharmonic Problem with Weighted Dirichlet Integral
Matevossian, Hovik A.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2024, 45 (08) : 3629 - 3645
[8] Smoothness of Solutions of the Dirichlet Problem for the Biharmonic Equation in Nonsmooth 2D Domains
Chichoyan, S. F.
MATHEMATICAL NOTES, 2015, 98 (5-6) : 999 - 1001
[9] Smoothness of solutions of the Dirichlet problem for the biharmonic equation in nonsmooth 2D domains
Chichoyan, S. F.
DIFFERENTIAL EQUATIONS, 2016, 52 (02) : 260 - 264
[10] Smoothness of solutions of the Dirichlet problem for the biharmonic equation in nonsmooth 2D domains
S. F. Chichoyan
Differential Equations, 2016, 52 : 260 - 264

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