tailieunhanh - Báo cáo hóa học: " Research Article ¨ The Reverse Holder Inequality for the Solution to p-Harmonic Type System"

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 ¨ The Reverse Holder Inequality for the Solution to p-Harmonic Type System | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 397340 15 pages doi 2008 397340 Research Article The Reverse Holder Inequality for the Solution to p-Harmonic Type System Zhenhua Cao 1 Gejun Bao 1 Ronglu Li 1 and Haijing Zhu2 1 Department of Mathematics Harbin Institute of Technology Harbin 150001 China 2 College of Mathematics and Physics Shan Dong Institute of Light Industry Jinan 250353 China Correspondence should be addressed to Gejun Bao baogj@ Received 6 July 2008 Revised 9 September 2008 Accepted 5 November 2008 Recommended by Shusen Ding Some inequalities to A-harmonic equation A x du d v have been proved. The A-harmonic equation is a particular form of p-harmonic type system A x a du b d v only when a 0 and b 0. In this paper we will prove the Poincare inequality and the reverse Holder inequality for the solution to the p-harmonic type system. Copyright 2008 Zhenhua Cao 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. 1. Introduction Recently amount of work about the A-harmonic equation for the differential forms has been done. In fact the A-harmonic equation is an important generalization of the p-harmonic equation in R p 1 and the p-harmonic equation is a natural extension of the usual Laplace equation see 1 for the details . The reverse Holder inequalities have been widely studied and frequently used in analysis and related fields including partial differential equations and the theory of elasticity see 2 . In 1999 Nolder gave the reverse Holder inequality for the solution to the A-harmonic equation in 3 and different versions of Caccioppoli estimates have been established in 4-6 . In 2004 D Onofrio and Iwaniec introduced the p-harmonic type system in 7 which is an important extension of the conjugate A-harmonic equation. In