MENU

You are here

Geometric regularity for (nonlinear) PDEs

Edgard A. Pimentel
Institution: 
PUC- Rio
Location: 
Luigi Stasi Seminar Room, ICTP
Schedule: 
Wednesday, July 4, 2018 - 16:00
Abstract: 

In this talk we examine the regularity theory of the solutions to a few examples of (nonlinear) PDEs. Arguing through a genuinely geometrical method, we produce regularity results in Sobolev and Hölder spaces, including some borderline cases. Our techniques relate a problem of interest to another one - for which a richer theory is available - by means of a geometric structure, e.g., a path. Ideally, information is transported along such a path, giving access to finer properties of the original equation. Our examples include elliptic and parabolic fully nonlinear problems, the Isaacs equation, degenerate examples and a double divergence model. We close the talk with a discussion on open problems and further directions of work.

Sign in