0000000001136426

AUTHOR

Aleksandra Zapadinskaya

showing 7 related works from this author

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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Generalized Dimension Distortion under Mappings of Sub-Exponentially Integrable Distortion

2010

We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane.

Integrable systemMathematics - Complex VariablesGeneral MathematicsModulota111Mathematical analysisData_MISCELLANEOUSComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONData_CODINGANDINFORMATIONTHEORY30C62Distortion (mathematics)Exponential growthDimension (vector space)TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYEuclidean geometryFOS: MathematicsComplex Variables (math.CV)Constant (mathematics)MathematicsMathematicsofComputing_DISCRETEMATHEMATICS
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Regularity and modulus of continuity of space-filling curves

2019

We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example. peerReviewed

regularityPartial differential equationspace-filling curvesFunctional analysisGeneral Mathematics010102 general mathematicsMathematical analysisSpace (mathematics)01 natural sciencesModulus of continuitymodulus0103 physical sciencesjatkuvuusfraktaalitmittateoria010307 mathematical physics0101 mathematicsAnalysisMathematicsJournal d'Analyse Mathématique
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Generalized dimension distortion under planar Sobolev homeomorphisms

2009

We prove essentially sharp dimension distortion estimates for planar Sobolev-Orlicz homeomorphisms.

Distortion (mathematics)Sobolev spaceMathematics::Functional AnalysisMathematics::Dynamical SystemsPlanarDimension (vector space)Applied MathematicsGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsMathematics::Analysis of PDEsMathematics::General TopologyMathematicsProceedings of the American Mathematical Society
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Generalized dimension estimates for images of porous sets under monotone Sobolev mappings

2014

We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porous sets under monotone Sobolev mappings, satisfying suitable Orlicz-Sobolev conditions.

Sobolev spaceMathematics::Functional AnalysisMonotone polygonDimension (vector space)Applied MathematicsGeneral MathematicsMathematical analysisMathematics::Analysis of PDEsSobolev inequalityMathematicsProceedings of the American Mathematical Society
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Generalized dimension distortion under Sobolev mappings

2011

dimensionmatematiikkaSobolev spacesHausdorff dimensionOrlicz spaces
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