Global integrability and weak Harnack estimates for elliptic PDEs in divergence form

Sirakov, Boyan

doi:10.2140/apde.2022.15.197

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Global integrability and weak Harnack estimates for elliptic PDEs in divergence form

Boyan Sirakov

Vol. 15 (2022), No. 1, 197–216

DOI: 10.2140/apde.2022.15.197

Abstract

We show that two classically known properties of positive supersolutions of uniformly elliptic PDEs, the boundary point principle (Hopf lemma) and global integrability, can be quantified with respect to each other. We obtain an extension up to the boundary of the De Giorgi–Moser weak Harnack inequality, optimal with respect to the norms involved, for equations in divergence form.

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Keywords

weak Harnack, Hopf lemma, global integrability, boundary estimates, elliptic PDE, divergence form

Mathematical Subject Classification 2010

Primary: 35B45, 35B50, 35B65, 35D30, 35J67

Milestones

Received: 11 February 2020

Revised: 10 June 2020

Accepted: 15 September 2020

Published: 16 March 2022

Authors

Boyan Sirakov
Departamento de Matemática Pontifícia Universidade Católica do Rio de Janeiro Rio de Janeiro Brazil

Vol. 15, No. 1, 2022