Galerkin approximations in problems with anisotropicp(·)-Laplacian
Svetlana Evgenievna Pastukhova, D. A. Yakubovich · Applicable Analysis · 2018
In this paper, we consider the Dirichlet problem in a bounded domain of Rd for an elliptic equation with an anisotropic p(·)-Laplace operator. Anisotropy is created by a measurable symmetric matrix A which stands under the divergence operator in the p(·)-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.