On solvability of the Dirichlet problem with the boundary function in Ln (2) for a second-order elliptic equation

摘要

We consider Dirichlet problems in a bounded domain Q aS, R (n) for a general secondorder elliptic equation with the boundary function in L (2). In the author's previous papers necessary and sufficient conditions for the existence of an (n - 1)-dimensionally continuous solution were obtained under some natural assumptions on the coefficients of equation. Those assumptions are formulated in terms of an auxiliary operator equation in a special Hilbert space and are difficult to verify. In the prese