6533b830fe1ef96bd1297b4a

RESEARCH PRODUCT

Dimension gap under Sobolev mappings

Pekka KoskelaAleksandra Zapadinskaya

subject

Mathematics::Functional AnalysisPure mathematicsquasihyperbolic distanceGeneral Mathematicsgeneralized Hausdorff measureMathematical analysista111Sobolev mappingHausdorff spaceConformal map16. Peace & justiceSobolev inequalitySobolev spaceDimension (vector space)Orlicz–Sobolev mappingMathematics

description

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.

yearjournalcountryeditionlanguage
2015-04-01Advances in Mathematics
10.1016/j.aim.2014.12.039http://juuli.fi/Record/0009143115