Vol. 15, No. 1, 2022

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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
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.

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