Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Local Regularity and Local Boundedness Results for Very Weak Solutions of Obstacle Problems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 878769 12 pages doi 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 1 College of Mathematics and Computer Science Hebei University Baoding 071002 China 2 Hebei Provincial Center of Mathematics Hebei Normal University Shijiazhuang 050016 China 3 College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China 4 Faculty of Science Huzhou Teachers College Huzhou Zhejiang 313000 China Correspondence should be addressed to Gao Hongya hongya-gao@ 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. Local regularity and local boundedness results for very weak solutions of obstacle problems of the A-harmonic equation div A x Vu x 0 are obtained by using the theory of Hodge decomposition where A x i p-1. 1. Introduction and Statement of Results Let Q be a bounded regular domain in R n 2. By a regular domain we understand any domain of finite measure for which the estimates for the Hodge decomposition in and are satisfied see 1 . A Lipschitz domain for example is a regular domain. We consider the second-order divergence type elliptic equation also called A-harmonic equation or Leray-Lions equation div A x Vu xf 0 where A x if Q X R R is a Caratheodory function satisfying the following conditions a AM if atf b A x i pur1 c A x 0 0 2 Journal of Inequalities and Applications where p 1 and 0 a Ộ TO. The prototype of is the p-harmonic equation div Vu p-2Vu 0. Suppose that w is an arbitrary function in Q with values in R u to and e e W1r Q with .
