Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form

2022/07/27 by Rendón, Fiorella, Sirakov, Boyan, Soares, Mayra · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.13679

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.

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• A quantitative Hopf-Oleinik lemma for degenerate fully nonlinear operators and applications to free boundary problems

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