6533b83afe1ef96bd12a7af2
RESEARCH PRODUCT
Boundary blow-up under Sobolev mappings
Pekka KoskelaAapo Kauranensubject
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 physics26B10Analysis26B35description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-01-01 | Analysis & PDE |