Galerkin approximations for singular linear elliptic and semilinear parabolic problems

Abstract

We prove the existence of exact solutions and convergence of numerical (Galerkin) approximations for the semilinear degenerate parabolic problem ut+Lu = F(t,u) and for the degenerate elliptic problem Lu = f where L is a highly singular linear elliptic operator. The class of operators L contains in particular the operators of generalized bi-axially symmetric potential theory.