Hölder continuity of ρ(x)-superharmonic functions

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13 Citations (Scopus)


In this paper we show that a solution of the equation -Δ ρ(x)u = μ is Hölder continuous with exponent α if and only if the nonnegative Radon measure μ satisfies the growth condition μ(Br(x))≤ Crn-ρ(x)+α(ρ(x)-1) for any ball Br(x)⊂ Ω, with r small enough. This extends an old result of Lewy and Stampacchia for the Laplace operator, and a recent result of Kilpelinen and Zhong for the p-Laplace operator with p constant.

Original languageEnglish
Pages (from-to)2433-2444
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number8
Publication statusPublished - Oct 15 2010
Externally publishedYes


  • ρ(x)-Laplace operator
  • ρ(x)-superharmonic functions
  • Hölder continuity
  • Radon measure
  • Variable exponent Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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