Search results for "boundary regularity"

showing 3 items of 3 documents

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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Boundary Regularity for the Porous Medium Equation

2018

We study the boundary regularity of solutions to the porous medium equation $u_t = \Delta u^m$ in the degenerate range $m>1$. In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for general -- not necessarily cylindrical -- domains in ${\bf R}^{n+1}$. One of our fundamental tools is a new strict comparison principle between sub- and superpara…

Pure mathematicsComplex systemBoundary (topology)Mathematical AnalysisCharacterization (mathematics)01 natural sciencesMathematics - Analysis of PDEsMathematics (miscellaneous)Matematisk analysporous medium equationFOS: Mathematics0101 mathematicsSpatial domainMathematicsosittaisdifferentiaaliyhtälötDirichlet problemMechanical Engineering010102 general mathematicsDegenerate energy levels35K20 (Primary) 35B51 35B65 35K10 35K55 35K65 (Secondary)010101 applied mathematicsRange (mathematics)boundary regularityPorous mediumAnalysisAnalysis of PDEs (math.AP)Archive for Rational Mechanics and Analysis
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Nonlinear balayage on metric spaces

2009

We develop a theory of balayage on complete doubling metric measure spaces supporting a Poincaré inequality. In particular, we are interested in continuity and p-harmonicity of the balayage. We also study connections to the obstacle problem. As applications, we characterize regular boundary points and polar sets in terms of balayage. Original Publication:Anders Björn, Jana Björn, Tero Mäkäläinen and Mikko Parviainen, Nonlinear balayage on metric spaces, 2009, Nonlinear Analysis, (71), 5-6, 2153-2171.http://dx.doi.org/10.1016/j.na.2009.01.051Copyright: Elsevier Science B.V., Amsterdam.http://www.elsevier.com/

Pure mathematicsMatematikBalayageApplied MathematicsMathematical analysisPoincaré inequalityBoundary (topology)Measure (mathematics)symbols.namesakeMetric spaceMetric (mathematics)Obstacle problemsymbolsBalayage; Boundary regularity; Continuity; Doubling measure; Metric space; Nonlinear; Obstacle problem; Perron solution; p-harmonic; Polar set; Poincaré inequality; Potential theory; SuperharmonicAnalysisMathematicsMathematicsPolar set (potential theory)
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