Thursday, December 11, 2025 — 12:00 pm — aula M2.5, edificio Matematica
Gradient regularity for strongly singular or degenerate elliptic and parabolic equations
Abstract: The aim of this seminar is to present recent advances in the regularity theory for weak solutions to some classes of elliptic and parabolic equations with strongly singular or degenerate structure. The equations under consideration satisfy standard $p$-growth and $p$-ellipticity conditions only outside a ball centered at the origin. In the elliptic setting, I will describe Besov and Sobolev regularity results for suitable nonlinear functions of the gradient of the weak solutions, covering both the subquadratic ($1<p<2$) and superquadratic ($p\geq2$) regimes. Analogous results are obtained in the corresponding parabolic framework, where I will address the higher spatial and temporal differentiability of the solutions under appropriate assumptions on the data.
This talk is based on joint work with Fabian Bäuerlein, Antonio Giuseppe Grimaldi and Antonia Passarelli di Napoli.