On a Dirichlet Problem for Properly Elliptic Equation in the Space of Continuous Functions

被引：0

作者：

A. H. Babayan ^{[1
]}

机构：

[1] National Polytechnic University of Armenia, Yerevan

[2] Regional Mathematical Center of Southern Federal University, Rostov-on-Don

来源：

Lobachevskii Journal of Mathematics | 2024年 / 45卷 / 12期

关键词：

defect numbers; Dirichlet problem; nontrivial solutions of the homogeneous Dirichlet problem; properly elliptic equation;

D O I：

10.1134/S1995080224607379

中图分类号：

学科分类号：

摘要：

Abstract: The Dirichlet problem for order properly elliptic equation with constant coefficients in the unit disc is considered. We seek the solution of the problem in the class of functions times continuously differentiable in the disc and continuous up to the boundary with the derivatives of order not more than. The necessary and sufficient conditions for solvability of this problem are obtained and if these conditions hold the solution is determined in explicit form. © Pleiades Publishing, Ltd. 2024.

引用

页码：6011 / 6026

页数：15

共 50 条

[31] On Boundary Values of Solutions of the Dirichlet Problem for Second Order Elliptic Equation
Dumanyan, V. Zh.
JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 2010, 45 (01): : 26 - 42
[32] On the Estimate of Integral Norm of Solution of the Dirichlet Problem for Quasilinear Elliptic Equation
S. V. Pikulin
Mathematical Notes, 2023, 114 : 639 - 642
[33] The Dirichlet Problem for an Elliptic Equation with Several Singular Coefficients in an Infinite Domain
Ergashev, T. G.
Tulakova, Z. R.
RUSSIAN MATHEMATICS, 2021, 65 (07) : 71 - 80
[34] Solvability of the Dirichlet problem for a general second-order elliptic equation
Dumanyan, V. Zh.
SBORNIK MATHEMATICS, 2011, 202 (07) : 1001 - 1020
[35] On the Estimate of Integral Norm of Solution of the Dirichlet Problem for Quasilinear Elliptic Equation
Pikulin, S. V.
MATHEMATICAL NOTES, 2023, 114 (3-4) : 639 - 642
[36] On the Solvability of the Dirichlet Problem for a Multidimensional Elliptic System in the Half-Space
Golovko E.A.
Journal of Mathematical Sciences, 2024, 279 (5) : 635 - 643
[37] On the dirichlet problem of extreme points for non-continuous functions
Jiří Spurný
Israel Journal of Mathematics, 2009, 173 : 403 - 419
[38] The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space
John Urbas
Calculus of Variations and Partial Differential Equations, 2003, 18 : 307 - 316
[39] The Dirichlet problem for a 3D elliptic equation with two singular coefficients
Karimov, E. T.
Nieto, J. J.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (01) : 214 - 224
[40] The Dirichlet Problem for an Elliptic Equation with Singular Coefficients in a Semi-Cylindrical Domain
A. K. Urinov
K. T. Karimov
Lobachevskii Journal of Mathematics, 2020, 41 : 1898 - 1909

← 1 2 3 4 5 →