Solvability of the Dirichlet problem for a general second-order elliptic equation

Abstract

The paper is concerned with studying the solvability of the Dirichlet problem for the second-order elliptic equation in a bounded domain , , with -smooth boundary and boundary condition .Conditions for the existence of an -dimensionally continuous solution are obtained, the resulting solvability condition is shown to be similar in form to the solvability condition in the conventional generalized setting (in ). In particular, the problem is shown to have an -dimensionally continuous solution for all and all and from the appropriate function spaces, provided that the homogeneous problem (with zero boundary conditions and zero right-hand side) has no nonzero solutions in .Bibliography: 14 titles.