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.
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页码：2570 / 2586
页数：17
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