Nonlocal operators related to nonsymmetric forms II: Harnack inequalities

Abstract

Local boundedness and Harnack inequalities are studied for solutions to parabolic and elliptic integro-differential equations whose governing nonlocal operators are associated with nonsymmetric forms. We present two independent proofs, one being based on the De Giorgi iteration and the other one on the Moser iteration technique. This article is a continuation of a recent work by the same authors, where Hölder regularity and a weak Harnack inequality are proved in a similar setup.

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• Inverse Problem for a Curved Quantum Guide
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• The second eigenvalue of the fractional $p-$Laplacian
• Local regularity for parabolic nonlocal operators
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• Regularity estimates for elliptic nonlocal operators