Harnack inequality for nonlocal problems with non-standard growth
Jamil Chaker, Minhyun Kim, Marvin Weidner
Abstract
Abstract We prove a full Harnack inequality for local minimizers, as well as weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are local boundedness and a weak Harnack inequality for functions in a corresponding De Giorgi class. This paper builds upon a recent work on regularity estimates for such nonlocal problems by the same authors.
Topics & Concepts
Harnack's inequalityMathematicsHarnack's principleInequalityClass (philosophy)Pure mathematicsWork (physics)Applied mathematicsMathematical analysisComputer scienceArtificial intelligenceMechanical engineeringEngineeringNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis