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arXiv · 1910.05160

Optimal boundary regularity for fast diffusion equations in bounded domains

Tianling Jin·Jingang Xiong
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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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Tianling Jin, Jingang Xiong. 2019-10-11. Optimal boundary regularity for fast diffusion equations in bounded domains. https://arxiv.org/abs/1910.05160

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