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Nonlinear Analysis

Optimal boundary regularity and extinction profiles for solutions  of fast diffusion equations in bounded domains

Jingang Xiong, Beijing Normal University

Location:  Hill 705
Date & time: Tuesday, 10 December 2019 at 1:40PM - 2:50PM

Abstract: I will first present the 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 uses a geometric type structure of the equations---evolution of a scalar curvature-like quantity.  Second, I will talk about soliton resolution of the Sobolev critical fast diffusion equation and a flow proof of the Brezis-Nirenberg theorem.

This is based on joint work with Tianling Jin.