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.

This is a much improved version of the older manuscript, thanks to the suggestions of the anonymous referee. The main revision is that we added three appendices to provide supplementary materials for the linear equation part. Also, Corollary 1.4 is improved from the suggestions of the anonymous referee

References in corpus (2)

• Bubbling and extinction for some fast diffusion equations in bounded domains
• Extinction behaviour for the fast diffusion equations with critical exponent and Dirichlet boundary conditions

Cited by in corpus (3)

• The Cauchy-Dirichlet Problem for Singular Nonlocal Diffusions on Bounded Domains
• Bubbling and extinction for some fast diffusion equations in bounded domains
• Infinite-time blowing-up solutions to small perturbations of the Yamabe flow