Galerkin approximations in problems with anisotropic p(·)-Laplacian. Issue 1 (25th January 2019)

• Record Type: Journal Article
• Authors: Pastukhova, S. E.; Yakubovich, D. A.
• Is Part Of: Applicable analysis. Volume 98:Issue 1/2(2019)
• Page Start: 345
• Page End: 361
• Publication Date: 2019-01-25
• Subjects: Galerkin approximations -- anisotropic Laplacian with variable exponent -- variable exponent spaces -- error estimate; 35J92 -- 35A35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1451641
• Languages: English
• ISSNs: 0003-6811

Abstract

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.