Regularity of solutions to the Dirichlet problem for fast diffusion equations

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-06-02 DOI:10.1016/j.aim.2025.110390

Tianling Jin , Jingang Xiong

引用次数: 0

Abstract

We prove global Hölder gradient estimates for bounded positive weak solutions of fast diffusion equations in smooth bounded domains with the homogeneous Dirichlet boundary condition, which then lead us to establish their optimal global regularity. This solves a problem raised by Berryman and Holland in 1980.

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快速扩散方程Dirichlet问题解的正则性

利用齐次Dirichlet边界条件证明了光滑有界区域上快速扩散方程有界正弱解的全局Hölder梯度估计，从而建立了它们的最优全局正则性。这解决了Berryman和Holland在1980年提出的一个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.