On the solvability conditions of the first boundary value problem for a system of elliptic equations that strongly degenerate at a point
Institute of Mathematics and Informatics of Vilnius University, Akademijos str. 4, LT-08863, Vilnius, Lithuania
Boundary Value Problems 2011, 2011:16 doi:10.1186/1687-2770-2011-16Published: 22 August 2011
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.