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

Fiorella Rendón; Boyan Sirakov; Mayra Soares

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arXiv · 2207.13679

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

Fiorella Rendón·Boyan Sirakov·Mayra Soares

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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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Fiorella Rendón, Boyan Sirakov, Mayra Soares. 2022-07-27. Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form. https://arxiv.org/abs/2207.13679

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