G.R. Mingione | Hopf, Caccioppoli and Schauder, reloaded
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 01/08/2022

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Guiseppe Rosario Mingione (University of Parmay) 
Hopf, Caccioppoli and Schauder, reloaded

So called Schauder estimates are in fact a contribution, at various stages, of
Hopf, Caccioppoli and Schauder, between the end of the 20s and the beginning of the 30s. Later on, they were extended, with various degrees of precision, to nonlinear uniformly elliptic equations. I will present the solution to the longstanding open problems of proving estimates of such kind in the nonuniformly elliptic case and for minima of nondifferentiable functionals (again considered in the nonuniformly elliptic case). From joint work with Cristiana De Filippis.