Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 163269, 16 pages
Research Article

Local Boundedness of Weak Solutions for Nonlinear Parabolic Problem with p(x)-Growth

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

Received 23 October 2009; Revised 6 January 2010; Accepted 29 January 2010

Academic Editor: Shusen Ding

Copyright © 2010 Yongqiang Fu and Ning Pan. 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 study the nonlinear parabolic problem with p(x)-growth conditions in the space W1,xLp(x)(Q) and give a local boundedness theorem of weak solutions for the following equation (u/t)+A(u)=0, where A(u)=diva(x,t,u,u)+a0(x,t,u,u),a(x,t,u,u) and a0(x,t,u,u) satisfy p(x)-growth conditions with respect to u and u.