Very degenerate elliptic equations under almost critical Sobolev regularity
Analysis of PDEs
2019-06-07 v2
Abstract
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.
Cite
@article{arxiv.1803.08723,
title = {Very degenerate elliptic equations under almost critical Sobolev regularity},
author = {Albert Clop and Raffaella Giova and Farhad Hatami and Antonia Passarelli di Napoli},
journal= {arXiv preprint arXiv:1803.08723},
year = {2019}
}