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Abstract and Applied Analysis
Volume 2013, Article ID 368610, 7 pages
Research Article

A New Extension of Serrin's Lower Semicontinuity Theorem

1School of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Mathematical College, Sichuan University, Chengdu 610064, China

Received 18 February 2013; Revised 3 June 2013; Accepted 3 June 2013

Academic Editor: Yisheng Song

Copyright © 2013 Xiaohong Hu and Shiqing Zhang. 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.


We present a new extension of Serrin's lower semicontinuity theorem. We prove that the variational functional defined on is lower semicontinuous with respect to the strong convergence in , under the assumptions that the integrand has the locally absolute continuity about the variable .