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Hölder continuity of solutions to quasilinear elliptic equations involving measures

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Abstract

We show that the solutionu of the equation

$$ - div(|\nabla u|^{p - 2} \nabla u) = \mu $$

is locally β-Hölder continuous provided that the measure μ satisfies the condition μ(B(x,r))⩽Mr n − p + α(p − 1) for some α>β. A corresponding result for more general operators is also proven.

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Authors and Affiliations

  1. Department of Mathematics, University of Jyväskylä, P.O. Box 35, 40351, Jyväskylä, Finland

    Tero Kilpeläinen

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  1. Tero Kilpeläinen
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Kilpeläinen, T. Hölder continuity of solutions to quasilinear elliptic equations involving measures. Potential Anal 3, 265–272 (1994). https://doi.org/10.1007/BF01468246

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  • DOI: https://doi.org/10.1007/BF01468246

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