Search results for "Harnack's principle"

showing 4 items of 4 documents

A tour of the theory of absolutely minimizing functions

2004

A detailed analysis of the class of absolutely minimizing functions in Euclidean spaces and the relationship to the infinity Laplace equation

Class (set theory)Pure mathematicsHarnack's principleApplied MathematicsGeneral MathematicsInfinity LaplacianEuclidean geometryCalculusHarnack's inequalityMathematicsBulletin of the American Mathematical Society
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The boundary Harnack inequality for infinity harmonic functions in Lipschitz domains satisfying the interior ball condition

2008

Abstract In this note, we give a short proof for the boundary Harnack inequality for infinity harmonic functions in a Lipschitz domain satisfying the interior ball condition. Our argument relies on the use of quasiminima and the notion of comparison with cones.

Harnack's principleLipschitz domainHarmonic functionApplied MathematicsMathematical analysisMathematics::Analysis of PDEsBall (mathematics)Lipschitz continuityAnalysisMathematicsHarnack's inequalityNonlinear Analysis: Theory, Methods & Applications
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A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term

2017

This paper concerns the boundary behavior of solutions of certain fully nonlinear equations with a general drift term. We elaborate on the non-homogeneous generalized Harnack inequality proved by the second author in (Julin, ARMA -15), to prove a generalized Carleson estimate. We also prove boundary H\"older continuity and a boundary Harnack type inequality.

Mathematics::Analysis of PDEsGeneralized Carleson estimateBoundary (topology)Hölder conditionnonlinear elliptic equations01 natural sciencesHarnack's principleMathematics - Analysis of PDEsMathematics::ProbabilityFOS: MathematicsNon-Lipschitz drift0101 mathematicsElliptic PDECarleson estimateHarnack's inequalityMathematics010102 general mathematicsMathematical analysista111Type inequalityLipschitz continuityTerm (time)010101 applied mathematicsNonlinear systemAnalysisAnalysis of PDEs (math.AP)
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Harnack's inequality for p-harmonic functions via stochastic games

2013

We give a proof of asymptotic Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Lipsc...

Pure mathematicsApplied Mathematics010102 general mathematicsMathematical analysista111Mathematics::Analysis of PDEs16. Peace & justiceLipschitz continuity01 natural sciences010101 applied mathematicsHarnack's principleHarmonic functionInfinity Laplacian0101 mathematicsEquivalence (measure theory)AnalysisHarnack's inequalityMathematicsCommunications in Partial Differential Equations
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