On the isomorphic mapping of weighted spaces by an elliptic operator with degeneration on the domain boundary

We consider the first boundary value problem for a second-order elliptic equation with degeneration on the entire twice continuously differentiable boundary of a two-dimensional domain Omega; this problem has a generalized solution in the weighted space W-2,alpha-1(2)(Omega). We find conditions ensuring that the generalized solution belongs to the narrower space W-2,alpha+lambda-1(2)(Omega) (-1/2 < alpha < alpha + lambda < 1/2), which permits obtaining estimates for the convergence rate of an approximate finite-element solution to the exact solution in the norms of the spaces W-2,alpha(1)(Omega) and L-2(Omega).