PARTIAL REGULARITY RESULT OF SUPERQUADRATIC ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS  

作　　者：Yalin Qiu 

机构地区：[1]School of Math.and Computing Science, Longyan University

出　　处：《Annals of Applied Mathematics》2017年第2期162-185,共24页应用数学年刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10976026);Natural Science Foundation of Fujian Province(2012D102)

摘　　要：We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of A-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal H¨older exponent for the derivative of the weak solutions on the regular set.We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of A-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal H¨older exponent for the derivative of the weak solutions on the regular set.

关 键 词：superquadratic elliptic systems controllable growth condition A-harmonic approximation optimal partial regularity 

分 类 号：O175.25[理学—数学]