Very degenerate elliptic equations under almost critical Sobolev regularity

Albert Clop, Raffaella Giova, Farhad Hatami, Antonia Passarelli di Napoli

Published 2018-03-23, updated 2019-06-06Version 2

We prove the local Lipschitz continuity and the higher differentiability of local minimizers of integral functionals with non autonomous integrand which is degenerate convex with respect to the gradient variable. The main novelty here is that the results are obtained assuming that the coefficients have weak derivative in an almost critical Zygmund class and the datum f is assumed to belong to the same Zygmund class.