有界域中快速扩散方程的最优边界正则性

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2019-10-11 DOI:10.1353/ajm.2023.0003

Tianling Jin, Jingang Xiong

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引用次数: 20

摘要

文摘：我们证明了光滑有界域中快速扩散方程有界正弱解的最优边界正则性。这解决了Berryman和Holland在1980年提出的亚临界和临界状态下这些方程的问题。我们的先验估计的证明使用了快速扩散方程的几何型结构，其中一个重要的组成部分是类似曲率的量的演化方程。

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Optimal boundary regularity for fast diffusion equations in bounded domains

Abstract:We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes. Our proof of the a priori estimates uses a geometric type structure of the fast diffusion equations, where an important ingredient is an evolution equation for a curvature-like quantity.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.