Galerkin approximations in problems with anisotropic p(·)-Laplacian. Issue 1 (25th January 2019) - Pastukhova, S. E.; Yakubovich, D. A.
ABSTRACT: In this paper, we consider the Dirichlet problem in a bounded domain ofR d for an elliptic equation with an anisotropicp ( · ) -Laplace operator. Anisotropy is created by a measurable symmetric matrix A which stands under the divergence operator in thep ( · ) -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.