Table of Contents
Chinese Journal of Mathematics
Volume 2014 (2014), Article ID 549051, 7 pages
http://dx.doi.org/10.1155/2014/549051
Research Article

An Approximation of Hedberg’s Type in Sobolev Spaces with Variable Exponent and Application

Department of Mathematics, Laboratory LAMA, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, BP 1796, 30000 Atlas Fez, Morocco

Received 20 February 2014; Accepted 4 April 2014; Published 29 April 2014

Academic Editor: Juntao Sun

Copyright © 2014 Abdelmoujib Benkirane et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to extend the usual framework of PDE with to include a large class of cases with , whose coefficient satisfies conditions (including growth conditions) which guarantee the solvability of the problem . This new framework is conceptually more involved than the classical one includes many more fundamental examples. Thus our main result can be applied to various types of PDEs such as reaction-diffusion equations, Burgers type equation, Navier-Stokes equation, and p-Laplace equation.