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Open Access Research

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

Stasys Rutkauskas

Author affiliations

Institute of Mathematics and Informatics of Vilnius University, Akademijos str. 4, LT-08863, Vilnius, Lithuania

Citation and License

Boundary Value Problems 2011, 2011:16  doi:10.1186/1687-2770-2011-16

Published: 22 August 2011

Abstract

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.

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