Potential Analysis

, Volume 2, Issue 3, pp 249–254 | Cite as

Hölder type quasicontinuity

  • Jan Malý
Article

Abstract

It is proved that a functionuLm,p(Rn) (which coincides with the Sobolev spaceW1,p(Rn) ifm=1) coincides with a Hölder continuous functionw outside a set of smallm,q-capacity, whereq<p. Moreover, ifm=1, then the functionw can be chosen to be close tou in theW1,p-norm.

Mathematics Subject Classifications (1991)

46E35 31B15 

Key words

Hölder continuity Sobolev spaces capacity 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Jan Malý
    • 1
  1. 1.Department of MathematicsCharles UniversityPraha 8Czechia

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