Search results for "Measure density condition"

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Sobolev embeddings, extensions and measure density condition

2008

AbstractThere are two main results in the paper. In the first one, Theorem 1, we prove that if the Sobolev embedding theorem holds in Ω, in any of all the possible cases, then Ω satisfies the measure density condition. The second main result, Theorem 5, provides several characterizations of the Wm,p-extension domains for 1<p<∞. As a corollary we prove that the property of being a W1,p-extension domain, 1<p⩽∞, is invariant under bi-Lipschitz mappings, Theorem 8.

Discrete mathematicsExtension operator010102 general mathematicsEberlein–Šmulian theoremMeasure density condition01 natural sciencesSobolev embeddingSobolev inequality010101 applied mathematicsSobolev spaceCorollarySobolev spaces0101 mathematicsInvariant (mathematics)AnalysisEdge-of-the-wedge theoremSobolev spaces for planar domainsMathematicsTrace operatorJournal of Functional Analysis
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Uniform measure density condition and game regularity for tug-of-war games

2018

We show that a uniform measure density condition implies game regularity for all 2 < p < ∞ in a stochastic game called “tug-of-war with noise”. The proof utilizes suitable choices of strategies combined with estimates for the associated stopping times and density estimates for the sum of independent and identically distributed random vectors. peerReviewed

Statistics and ProbabilityIndependent and identically distributed random variablesComputer Science::Computer Science and Game Theorygame regularitydensity estimate for the sum of i.i.d. random vectorsTug of war01 natural sciencesMeasure (mathematics)$p$-regularityMathematics - Analysis of PDEsFOS: MathematicsApplied mathematicspeliteoriastochastic games0101 mathematics91A15 60G50 35J92Mathematicsp-harmonic functionsstokastiset prosessit$p$-harmonic functionsosittaisdifferentiaaliyhtälöthitting probability010102 general mathematicsStochastic gametug-of-war gamesProbability (math.PR)uniform measure density condition010101 applied mathematicsNoiseuniform distribution in a ballMathematics - ProbabilityAnalysis of PDEs (math.AP)
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