REGULARITY OF WEAK SOLUTIONS TO A CLASS OF NONLINEAR PROBLEM

• 作者: Jianfeng ZHOU Zhong TAN
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（4）
• 页码范围: 1333-1365
• 页数: 33页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.04.019

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 H(o)lder continuous with any exponent α ∈ (0,1) outside a singular set with zero parabolic measure.In particular,we prove that the regularity point in QT 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 Du,and at this stage,we obtain the Hausdorff dimension of a singular set of u.