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Journal of Function Spaces
Volume 2014, Article ID 435247, 9 pages
http://dx.doi.org/10.1155/2014/435247
Research Article

Nonlocal Variational Principles with Variable Growth

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 17 January 2014; Accepted 6 March 2014; Published 7 April 2014

Academic Editor: Qingying Bu

Copyright © 2014 Yongqiang Fu and Miaomiao Yang. 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

This paper is concerned with the functional defined by , where is a regular open bounded set and is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation of .