Erwin Topp Paredes

Universidade Federal do Rio de Janeiro, Brazil

Title: "Recycling" Ishii-Lions method for nonlocal problems.

Abstract: In this talk, I will report some regularity results for fractional elliptic equations through the celebrated Ishii-Lions method (JDE'90). We start discussing the original argument introduced in the early nineties for second-order problems, and the subsequent nonlocal analog proposed by Barles, Chasseigne and Imbert (JEMS'11). Following this last approach, our main contributions are a) Lipschitz regularity for unbounded solutions for fractional Hamilton-Jacobi equations; b) Liouville-type results for general fractional Hamilton-Jacobi, and reaction diffusion equations; and c) Lipshitz estimates for the (variational) fractional p-Laplacian. Joint work with Anup Biswas (IISER-Pune, India) and Alexander Quaas (UTFSM, Chile).