REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE: 1 m <2

doi:10.1016/S0252-9602(12)60151-9

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1937-1958.doi: 10.1016/S0252-9602(12)60151-9

REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE: 1 <m <2

邱亚林

School of Mathematics and Computing Science, Longyan University, Longyan 361005, China

收稿日期:2011-01-24 修回日期:2011-04-24 出版日期:2012-09-20 发布日期:2012-09-20
基金资助:
Supported by National Natural Science Foundation of China (10976026) and the Education Department of Fujian Province (JK2009045).

REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE: 1 <m <2

QIU Ya-Lin

School of Mathematics and Computing Science, Longyan University, Longyan 361005, China

Received:2011-01-24 Revised:2011-04-24 Online:2012-09-20 Published:2012-09-20
Supported by:
Supported by National Natural Science Foundation of China (10976026) and the Education Department of Fujian Province (JK2009045).

摘要/Abstract

摘要：

In this article, we consider interior regularity for weak solutions to nonlinear elliptic systems of divergence type with Dini continuous coefficients under natural growth condition for the case 1 < m < 2. All estimates in the case of m ≥ 2 is no longer suitable, and we can’t obtain the Caccioppoli’s second inequality by using these techniques developed in the case of m ≥ 2. But the Caccioppoli’s second inequality is the key to use A-harmonic approximation method. Thus, we adopt another technique introduced by Acerbi and Fcsco to overcome the difficulty and we also overcome those difficulties due to Dini condition. And then we apply the A-harmonic approximation method to prove partial regularity of weak solutions.

关键词: nonlinear elliptic systems, natural growth condition, partial regularity, A-harmonic approximation technique

Abstract:

Key words: nonlinear elliptic systems, natural growth condition, partial regularity, A-harmonic approximation technique

中图分类号:

35J45

邱亚林. REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE: 1 <m <2[J]. 数学物理学报(英文版), 2012, 32(5): 1937-1958.

QIU Ya-Lin. REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE: 1 <m <2[J]. Acta mathematica scientia,Series B, 2012, 32(5): 1937-1958.

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REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE: 1 <m <2

REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE: 1 <m <2

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