# Seminars & Colloquia Calendar

Nonlinear Analysis

## On the differentiability of solutions to fully nonlinear degenerate elliptic PDEs

#### Eduardo Teixeira, University of Central Florida

Location:  Zoom
Date & time: Wednesday, 02 March 2022 at 9:30AM - 10:30AM

Abstract: I will discuss nonlinear diffusion processes involving diffusion resistance. Mathematically one is led to consider fully nonlinear elliptic equations whose ellipticity degenerate as a function of the gradient; the law of degeneracy of the system. For non-degenerate models, a classical theorem proven independently by Caffarelli and Trudinger in the late 80â€™s assures that solutions are of class $$C^{1,alpha}$$ and a recent theorem proven by Imbert and Silvestre yields Holder continuity of solutions â€œindependentlyâ€ of the law of degeneracy. We want to understand the difficult borderline case regarding $$C^{1}$$ regularity.