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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 80’s assures that solutions are of class \(C^{1,alpha}\) and a recent theorem proven by Imbert and Silvestre yields Holder continuity of solutions “independently” of the law of degeneracy. We want to understand the difficult borderline case regarding \(C^{1}\) regularity.

Zoom link:
Meeting ID:964 3090 5091Passcode:491508

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