Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 878769, 12 pages
doi:10.1155/2010/878769
Research Article

Local Regularity and Local Boundedness Results for Very Weak Solutions of Obstacle Problems

Gao Hongya,1,2 Qiao Jinjing,3 and Chu Yuming4

1College of Mathematics and Computer Science, Hebei University, Baoding 071002, China
2Hebei Provincial Center of Mathematics, Hebei Normal University, Shijiazhuang 050016, China
3College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
4Faculty of Science, Huzhou Teachers College, Huzhou, Zhejiang 313000, China

Received 25 September 2009; Accepted 18 March 2010

Academic Editor: Yuming Xing

Copyright © 2010 Gao Hongya 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

Local regularity and local boundedness results for very weak solutions of obstacle problems of the 𝒜-harmonic equation div⁡𝒜(x,∇u(x))=0 are obtained by using the theory of Hodge decomposition, where |𝒜(x,ξ)|≈|ξ|p-1.