OPTIMAL BOUNDARY REGULARITY FOR FAST DIFFUSION EQUATIONS IN BOUNDED DOMAINS

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.

Automated summary

We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains, answering a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes. Our proof utilizes a geometric type structure of the fast diffusion equations, where an important component is an evolution equation for a curvature-like quantity.