SPRING 2021 Nonlinear Analysis Special Lecture Series
Professor Giuseppe Mingione, University of Parma
Title: Perturbations beyond Schauder
So-called Schauder estimates are a standard tool in the analysis of linear elliptic and parabolic PDEs. They had been proved by Hopf (1929 interior case), and by Scahuder and Caccioppoli (1934, global estimates). Since then, several proofs have been given (Campanato, Trudinger, Simon). The nonlinear case is a more recent achievement from the 80s (Giaquinta \& Giusti, Ivert, J. Manfredi, Lieberman). All these classical results take place in the uniformly elliptic case.
I will discuss progress in the nonuniformly elliptic one. From recent, joint work with Cristiana De Filippis (Torino).