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  • The recent result shows that a homeomorphism $f\in W^{1,n-1}_{\loc}(\Omega,\rn)$ of finite distortion satisfies $f^{-1}\in W^{1,1}_{\loc}(f(\Omega),\rn)$. We show that this result is sharp in a sense that the crutial regularity condition $|Df|\in L^{n-1}$ cannot be replaced by $|\adj Df|\in L^1$ or by a requirement that $|Df|$ belongs to some bigger Orlicz space.
  • The recent result shows that a homeomorphism $f\in W^{1,n-1}_{\loc}(\Omega,\rn)$ of finite distortion satisfies $f^{-1}\in W^{1,1}_{\loc}(f(\Omega),\rn)$. We show that this result is sharp in a sense that the crutial regularity condition $|Df|\in L^{n-1}$ cannot be replaced by $|\adj Df|\in L^1$ or by a requirement that $|Df|$ belongs to some bigger Orlicz space. (en)
Title
  • Sharpness of the assumptions for the regularity of a homeomorphism
  • Sharpness of the assumptions for the regularity of a homeomorphism (en)
skos:prefLabel
  • Sharpness of the assumptions for the regularity of a homeomorphism
  • Sharpness of the assumptions for the regularity of a homeomorphism (en)
skos:notation
  • RIV/00216208:11320/10:10050521!RIV11-MSM-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 59
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 287177
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/10:10050521
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Sobolev space (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [B2E12D53EC77]
http://linked.open...i/riv/nazevZdroje
  • Michigan Mathematical Journal
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2010
http://linked.open...iv/tvurceVysledku
  • Hencl, Stanislav
http://linked.open...n/vavai/riv/zamer
issn
  • 0026-2285
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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