Affordable Access

Access to the full text

Regularity of Weak Solutions to a Class of Nonlinear Problem

Authors
  • Zhou, Jianfeng1
  • Tan, Zhong2
  • 1 Peking University, Beijing, 100871, China , Beijing (China)
  • 2 Xiamen University, Xiamen, 361005, China , Xiamen (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 01, 2021
Volume
41
Issue
4
Pages
1333–1365
Identifiers
DOI: 10.1007/s10473-021-0419-3
Source
Springer Nature
Keywords
License
Yellow

Abstract

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 Hölder 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.

Report this publication

Statistics

Seen <100 times