Search results for "Sobolev mapping"

showing 4 items of 4 documents

Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

2010

Abstract We investigate how the integrability of the derivatives of Orlicz–Sobolev mappings defined on open subsets of R n affect the sizes of the images of sets of Hausdorff dimension less than n. We measure the sizes of the image sets in terms of generalized Hausdorff measures.

Mathematics::Functional AnalysisPure mathematicsApplied Mathematicsta111Hausdorff spaceMathematics::General Topology30C62Measure (mathematics)Image (mathematics)Dimension distortionMappings of finite distortionDistortion (mathematics)Sobolev spaceMathematics - Classical Analysis and ODEsHausdorff dimensionEuclidean geometryClassical Analysis and ODEs (math.CA)FOS: MathematicsSobolev mappingsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Dimension gap under Sobolev mappings

2015

Abstract We prove an essentially sharp estimate in terms of generalized Hausdorff measures for the images of boundaries of Holder domains under continuous Sobolev mappings, satisfying suitable Orlicz–Sobolev conditions. This estimate marks a dimension gap, which was first observed in [2] for conformal mappings.

Mathematics::Functional AnalysisPure mathematicsquasihyperbolic distanceGeneral Mathematicsgeneralized Hausdorff measureMathematical analysista111Sobolev mappingHausdorff spaceConformal map16. Peace & justiceSobolev inequalitySobolev spaceDimension (vector space)Orlicz–Sobolev mappingMathematicsAdvances in Mathematics
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Boundary blow-up under Sobolev mappings

2014

We prove that for mappings $W^{1,n}(B^n, \R^n),$ continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero $n$-Hausdorff measure. For H\"older continuous mappings we also prove an essentially sharp generalized Hausdorff dimension estimate.

Unit spherePure mathematicsSobolev mappingBoundary (topology)01 natural sciencesMeasure (mathematics)Hausdorff measureModulus of continuitymodulus of continuity0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics46E35Hausdorff measure0101 mathematicsMathematicsNumerical AnalysisApplied Mathematicsta111010102 general mathematicsZero (complex analysis)Sobolev spaceMathematics - Classical Analysis and ODEsHausdorff dimension010307 mathematical physics26B10Analysis26B35Analysis & PDE
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Sharpness of the differentiability almost everywhere and capacitary estimates for Sobolev mappings

2017

We give sharp conformal conditions for the dfferentiability in the Sobolev space W1, n-1 loc (Ω,Rn). Furthermore, we show that the space W1, n-1 loc (Ω,Rn) can be considered as the borderline space for some capacitary inequalities. peerReviewed

capacitymapping of finite distortionSobolev mappingsdifferentiability
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