Nonlocal operators related to nonsymmetric forms, II: Harnack inequalities

Kassmann, Moritz; Weidner, Marvin

doi:10.2140/apde.2024.17.3189

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Nonlocal operators related to nonsymmetric forms, II: Harnack inequalities

Moritz Kassmann and Marvin Weidner

Vol. 17 (2024), No. 9, 3189–3249

DOI: 10.2140/apde.2024.17.3189

Abstract

Local boundedness and Harnack inequalities are studied for solutions to parabolic and elliptic integrodifferential equations whose governing nonlocal operators are associated with nonsymmetric forms. We present two independent proofs, one based on the De Giorgi iteration and the other on the Moser iteration technique. This article is a continuation of work of Kassmann and Weidner (2022), where Hölder regularity and a weak Harnack inequality are proved in a similar setup.

Keywords

nonlocal operator, energy form, nonsymmetric, regularity, Harnack inequality, De Giorgi, Moser

Mathematical Subject Classification

Primary: 31B05, 35B65, 35K90, 47G20, 60J76

Milestones

Received: 11 May 2022

Revised: 17 June 2023

Accepted: 14 August 2023

Published: 1 November 2024

Authors

Moritz Kassmann
Fakultät für Mathematik Universität Bielefeld Bielefeld Germany

Marvin Weidner
Departament de Matemàtiques i Informàtica Universitat de Barcelona Barcelona Spain

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Vol. 17, No. 9, 2024