Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form
Analysis of PDEs
2022-11-03 v2
Abstract
We obtain a global extension of the classical weak Harnack inequality which extends and quantifies the Hopf-Oleinik boundary-point lemma, for uniformly elliptic equations in divergence form. Among the consequences is a boundary gradient estimate, due to Krylov and well-studied for non-divergence form equations, but completely novel in the divergence framework. Another consequence is a new more general version of the Hopf-Oleinik lemma.
Cite
@article{arxiv.2207.13679,
title = {Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form},
author = {Fiorella Rendón and Boyan Sirakov and Mayra Soares},
journal= {arXiv preprint arXiv:2207.13679},
year = {2022}
}
Comments
19 pages; some misprints corrected, the proof of Theorem 1.2 was clarified and simplified