Special Session 74: Recent advances in local and nonlocal PDEs

Regularity estimates for 0-order p-Laplacian evolution problems
Ariel Salort
CEU San Pablo, Madrid
Spain
Co-Author(s):    Matteo Bonforte
Abstract:
We establish novel smoothing estimates and enhanced temporal regularity for a class of nonlinear nonlocal operators, characterized as order zero $p$-Laplacians. A key finding of this work is that the linear evolution ($p=2$) fails to satisfy the smoothing estimates that we prove to exist for the nonlinear regime. Furthermore, we demonstrate that these evolutions preserve local spatial regularity up to order $p$. This is a joint work with M. Bonforte (UAM, Spain).