Galerkin approximations in problems with anisotropic p(center dot)-Laplacian

摘要

In this paper, we consider the Dirichlet problem in a bounded domain of Rd for an elliptic equation with an anisotropic p(center dot)-Laplace operator. Anisotropy is created by a measurable symmetric matrix A which stands under the divergence operator in the p(center dot)-Laplacian. A Cordes-type condition is imposed on the matrix A to ensure the monotonicity property of the operator. We study the so-called variational solutions to the Dirichlet problem and construct Galerkin approximations for them. We estimate the difference between the exact and approximate solutions and the difference between corresponding flows.