Special Session 15: Qualitative properties for solutions to nonlinear elliptic and parabolic equations

Stability of Sobolev inequality and Sobolev equation in the endpoint case.
Lu Chen
Beijing Institute of Technology
Chile
Co-Author(s):    
Abstract:
In this talk, I will first revisit some new progress on the optimal stability of geometric inequality including Sobolev inequality, HLS inequality and fractional Sobolev inequality etc. Then I will present our recent results on the stability of Sobolev inequality and Sobolev equation in the end-point case. Finally, I will explain the relationship between these quantitative stability inequality and Aubin` conjecture, Chang-Yang conjecture, Keller-Segel equation