6533b7d7fe1ef96bd1268495

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Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

Thomas ZürcherAleksandra ZapadinskayaTapio Rajala

subject

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 mappingsAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2010-07-13Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2011.05.073