0000000000548679

AUTHOR

Benny Avelin

0000-0002-1429-4965

showing 5 related works from this author

Lower semicontinuity of weak supersolutions to the porous medium equation

2013

Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower semicontinuous after redefinition on a set of measure zero. This shows that weak supersolutions belong to a class of supersolutions defined by a comparison principle.

Degenerate diffusion35K55 31C45Applied MathematicsGeneral MathematicsMathematical analysista111Mathematics::Analysis of PDEscomparison principlelower semicontinuitysupersolutionsMathematics - Analysis of PDEsporous medium equationFOS: MathematicsPorous mediumdegenerate diffusionSign (mathematics)MathematicsAnalysis of PDEs (math.AP)
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Approximation of plurisubharmonic functions

2015

We extend a result by Fornaaess and Wiegerinck [Ark. Mat. 1989;27:257-272] on plurisubharmonic Mergelyan type approximation to domains with boundaries locally given by graphs of continuous functions.

Numerical AnalysisPure mathematicsApplied Mathematics010102 general mathematicsMathematical analysista111Type (model theory)01 natural sciences010101 applied mathematicsComputational Mathematicsboundary regularityMergelyan type approximationcontinuous boundaryplurisubharmonic functions0101 mathematicsapproximationAnalysisMathematicsComplex Variables and Elliptic Equations
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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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Variational parabolic capacity

2015

We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.

p-parabolic equationcapacityApplied Mathematicsta111Mathematical analysisDegenerate energy levelsMathematics::Analysis of PDEsContext (language use)Parabolic cylinder functionType (model theory)Parabolic partial differential equationHeat capacityNonlinear systemdegenerate parabolic equationsnonlinear potential theoryDiscrete Mathematics and CombinatoricsAnalysisComputer Science::Information TheoryMathematicsDiscrete and Continuous Dynamical Systems
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Harnack estimates for degenerate parabolic equations modeled on the subelliptic $p-$Laplacian

2014

Abstract We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype ∂ t u = − ∑ i = 1 m X i ⁎ ( | X u | p − 2 X i u ) where p ⩾ 2 , X = ( X 1 , … , X m ) is a system of Lipschitz vector fields defined on a smooth manifold M endowed with a Borel measure μ, and X i ⁎ denotes the adjoint of X i with respect to μ. Our estimates are derived assuming that (i) the control distance d generated by X induces the same topology on M ; (ii) a doubling condition for the μ-measure of d-metric balls; and (iii) the validity of a Poincare inequality involving X and μ. Our results extend the recent work in [16] , [36] , to a more general setting including the model cases of (1)…

Mathematics - Differential GeometryPure mathematicsGeneral MathematicsMathematics::Analysis of PDEsPoincaré inequalityVolume formsymbols.namesakeMathematics - Analysis of PDEsMathematics - Metric GeometryFOS: MathematicsP-LAPLACIAN OPERATORBorel measureRicci curvatureMathematicsHarnack's inequalityMatematikLebesgue measureta111HORMANDER VECTOR FIELDSMetric Geometry (math.MG)Lipschitz continuity35H20Differential Geometry (math.DG)p-LaplaciansymbolsHARNACK INEQUALITYMathematicsAnalysis of PDEs (math.AP)
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