Regularity of solutions to the Dirichlet problem for fast diffusion equations

Tianling Jin; Jingang Xiong

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arXiv · 2201.10091

Regularity of solutions to the Dirichlet problem for fast diffusion equations

Tianling Jin·Jingang Xiong

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Abstract

We prove global H\"older 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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Tianling Jin, Jingang Xiong. 2022-01-25. Regularity of solutions to the Dirichlet problem for fast diffusion equations. https://arxiv.org/abs/2201.10091

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