REGULARITY OF WEAK SOLUTIONS TO A CLASS OF NONLINEAR PROBLEM  

作　　者：Jianfeng ZHOU Zhong TAN 周建丰;谭忠(School of Mathematical Sciences,Peking University,Beijing 100871,China;School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China [2]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China

出　　处：《Acta Mathematica Scientia》2021年第4期1333-1365,共33页数学物理学报（B辑英文版）

基　　金：The first author is partially supported by the Postdoctoral Science Foundation of China(2019TQ0006);the second author is partially supported by the National Natural Science Foundation of China(11726023,11531010).

摘　　要：We study the regularity of weak solutions to a class of second order parabolic system under only the assumption of continuous coefficients.We prove that the weak solution u to such system is locally Holder continuous with any exponent α∈(0,1)outside a singular set with zero parabolic measure.In particular,we prove that the regularity point in Q_(T) is an open set with full measure,and we obtain a general criterion for the weak solution to be regular in the neighborhood of a given point.Finally,we deduce the fractional time and fractional space differentiability of D_(u),and at this stage,we obtain the Hausdorff dimension of a singular set of u.

关 键 词：Parabolic system REGULARITY weak solution HausdorfF dimension 

分 类 号：O175.26[理学—数学]