Abstract:  In this talk, I will discuss the modulus of continuity estimates for quasilinear and fully nonlinear parabolic equations: the moduli of continuity of solutions to parabolic equations are sub-solutions of suitable equations of one space variable. Then I will discuss two main applications:  sharp time-interior gradient estimates and lower bounds of the first nonzero eigenvalue of the Laplacian and p-Laplacian on manifolds.

 

The talk is based on several works, some of which are joint work with Dr. Kui Wang at Soochow University.

 

 

Host: Yuming Paul Zhang