On the solvability conditions of the first boundary value problem for a system of elliptic equations that strongly degenerate at a point

Boundary value problems

Stasys Rutkauskas¹ 

[1] Institute of Mathematics and Informatics of Vilnius University, Vilnius, Lithuania

关键词: systems of elliptic equations;    degenerate elliptic equations;    boundary value problems;    Dirichlet type problem;   

DOI  :  10.1186/1687-2770-2011-16

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A system of elliptic equations which are irregularly degenerate at an inner point is considered in this article. The equations are weakly coupled by a matrix that has multiple zero eigenvalue and corresponding to it adjoint vectors. Two statements of a well-posed Dirichlet type problem in the class of smooth functions are given and sufficient conditions on the existence and uniqueness of the solutions are obtained.

【 授权许可】

CC BY