当前位置: X-MOL 学术Acta Math. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Regularity of Weak Solutions to a Class of Nonlinear Problem
Acta Mathematica Scientia ( IF 1.2 ) Pub Date : 2021-06-01 , DOI: 10.1007/s10473-021-0419-3
Jianfeng Zhou , Zhong Tan

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.



中文翻译:

一类非线性问题弱解的正则性

我们研究了仅在连续系数假设下一类二阶抛物线系统弱解的规律性。我们证明了这种系统的弱解u是局部 Hölder 连续的,并且具有零抛物线测度的奇异集之外的任何指数α ∈ (0, 1)。特别地,我们证明了Q T中的正则点是一个全测度的开集,并且我们得到了弱解在给定点的邻域内是正则的一般准则。最后,我们推导了Du的分数时间和分数空间可微性,在这个阶段,我们得到了u的奇异集的Hausdorff 维数。

更新日期:2021-06-01
down
wechat
bug