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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
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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