The parabolic Harnack inequality for nonlocal equations
Moritz Kaßmann, Marvin Weidner
Abstract
We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable coefficients. Within the variational framework we prove the parabolic Harnack inequality and Hölder regularity estimates. We discuss in detail the shortcomings of previous results in this direction. The key element of our approach is a fine study of the nonlocal tail term.
Topics & Concepts
Harnack's inequalityHarnack's principleMathematicsMathematical analysisInequalityParabolic partial differential equationPartial differential equationDifferential Equations and Boundary ProblemsNonlinear Partial Differential EquationsNumerical methods in inverse problems