Maria-Magdalena Boureanu, Cristian Udrea, Diana-Nicoleta Udrea
Abstract:
We study a general class of anisotropic problems involving
-Laplace
type operators.
We search for weak solutions that are constant on the boundary
by introducing a new subspace of the anisotropic Sobolev space with
variable exponent and by proving that it is a reflexive Banach space.
Our argumentation for the existence of weak solutions is mainly based
on a variant of the mountain pass theorem of Ambrosetti and Rabinowitz.
Submitted April 8, 2013. Published October 4, 2013.
Math Subject Classifications: 35J25, 46E35, 35D30, 35J20.
Key Words: Anisotropic variable exponent Sobolev spaces;
Dirichlet problem; existence of weak solutions; mountain pass theorem.
A corrigendum was posted on December 23, 2013. It adds a condition to the original problem, and adds six references. See the last page of this article.
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Maria-Magdalena Boureanu Department of Applied Mathematics University of Craiova 200585 Craiova, Romania email: mmboureanu@yahoo.com |
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Cristian Udrea Department of Applied Mathematics University of Craiova 200585 Craiova, Romania email: udrea.cristian2013@yahoo.com |
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Diana-Nicoleta Udrea Department of Mathematics University of Craiova 200585 Craiova, Romania email: diannannicole@yahoo.com |
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