Optimal boundary regularity for fast diffusion equations in bounded domains
Tianling Jin, Jingang Xiong · American Journal of Mathematics · 2023
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.