Anne Bronzi : Regularity theory for a class of variable-exponent fully nonlinear elliptic equations

Posted by Ian Tobasco , part of the Analysis and Applied Mathematics Seminar.

At

Nov. 25, 2019, 4 p.m.

In

636 SEO

Abstract

In this talk we will explore the regularity of viscosity solutions for a class of variable-exponent, degenerate/singular elliptic equations in non-divergence form. More precisely, we will prove that viscosity solutions to the equation $|Du|^{p(x)}F(D^2u) = f(x)$, where $F$ is a uniformly elliptic operator and $p$ satisfies mild conditions, are locally of class $C^{1,\alpha}$. This is joint work with E. Pimentel (PUC-Rio), G. Rampasso (Unicamp) and E. Teixeira (UCF).