LOCAL CONTINUITY OF WEAK SOLUTIONS TO THE STEFAN PROBLEM INVOLVING THE SINGULAR p-LAPLACIAN

被引：1

作者：

Liao, Naian ^{[1
]}

机构：

[1] Univ Salzburg, Fachbereich Math, Hellbrunner Str 34, A-5020 Salzburg, Austria

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2022年 / 54卷 / 02期

关键词：

Stefan problem; parabolic p-Laplacian; local continuity; intrinsic scaling; expansion of positivity; TEMPERATURE;

D O I：

10.1137/21M1402443

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the local continuity of locally bounded weak solutions (temperatures) to the doubly singular parabolic equation modeling the phase transition of a material: \partial t\beta (u) - \Delta pu 3 N+1 < p < 2, where \beta is a maximal monotone graph with a jump at zero and \Delta p is the p-Laplacian. Moreover, a logarithmic type modulus of continuity is quantified, which has been conjectured to be optimal.

引用

页码：2570 / 2586

页数：17

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