Search results for "26B10"

showing 2 items of 2 documents

Differentiability in the Sobolev space W1,n-1

2014

Let Ω ⊂ Rn be a domain, n ≥ 2. We show that a continuous, open and discrete mapping f ∈ W1,n−1 loc (Ω, Rn ) with integrable inner distortion is differentiable almost everywhere on Ω. As a corollary we get that the branch set of such a mapping has measure zero. peerReviewed

46E3528A526B1030C65
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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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