tailieunhanh - báo cáo hóa học:" Research Article Hardy-Littlewood and Caccioppoli-Type Inequalities for A-Harmonic Tensors"

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 Hardy-Littlewood and Caccioppoli-Type Inequalities for A-Harmonic Tensors | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 351597 14 pages doi 2010 351597 Research Article Hardy-Littlewood and Caccioppoli-Type Inequalities for A-Harmonic Tensors Peilin Shi1 and Shusen Ding2 1 Department of Epidemiology Harvard School of Public Health Harvard University Boston mA 02115 UsA 2 Department of Mathematics Seattle University Seattle WA 98122 USA Correspondence should be addressed to Peilin Shi pshi@ Received 21 December 2009 Revised 17 March 2010 Accepted 19 March 2010 Academic Editor Yuming Xing Copyright 2010 P. Shi and S. Ding. 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 prove the new versions of the weighted Hardy-Littlewood inequality and Caccioppoli-type inequality for A-harmonic tensors. We also explore applications of our results to K-quasiregular mappings and p-harmonic functions in R . 1. Introduction The purpose of this paper is to prove the new versions of the weighted Hardy-Littlewood and Caccioppoli-type inequalities for the A-harmonic tensors. Our results may have applications in different fields particularly in the study of the integrability of solutions to the A-harmonic equation in some domains. Roughly speaking the A-harmonic tensors are solutions of the A-harmonic equation which is intimately connected to the fields including potential theory quasiconformal mappings and the theory of elasticity. The investigation of the A-harmonic equation has developed rapidly in the recent years see 1-11 . In this paper we still keep using the standard notations and symbols. All notations and definitions involved in this paper can be found in 1 cited in the paper. We always assume that M is a bounded and convex domain in Rn n 2. We write R R1. Let e1 e2 . en be the standard unit basis of Rn and Az Az Rn