Local boundedness and Harnack inequality for solutions of linear non-uniformly elliptic equations
Analysis of PDEs
2019-01-24 v1
Abstract
We study local regularity properties for solutions of linear, non-uniformly elliptic equations. Assuming certain integrability conditions on the coefficient field, we prove local boundedness and Harnack inequality. The assumed integrability assumptions are essentially sharp and improve upon classical results by Trudinger [ARMA 1971]. We then apply the deterministic regularity results to the corrector equation in stochastic homogenization and establish sublinearity of the corrector.
Keywords
Cite
@article{arxiv.1901.07958,
title = {Local boundedness and Harnack inequality for solutions of linear non-uniformly elliptic equations},
author = {Peter Bella and Mathias Schäffner},
journal= {arXiv preprint arXiv:1901.07958},
year = {2019}
}