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Singular solutions top-Laplacian type equations

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Arkiv för Matematik

Abstract

We construct singular solutions to equations

$$div\mathcal{A}(x,\nabla u) = 0,$$

similar to thep-Laplacian, that tend to ∞ on a given closed set ofp-capacity zero. Moreover, we show that everyG δ-set of vanishingp-capacity is the infinity set of someA-superharmonic function.

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Authors and Affiliations

  1. Department of Mathematics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40351, Jyväskylä, Finland

    Tero Kilpeläinen

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  1. Tero Kilpeläinen
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The research is financed by the Academy of Finland (Project #8597).

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Kilpeläinen, T. Singular solutions top-Laplacian type equations. Ark. Mat. 37, 275–289 (1999). https://doi.org/10.1007/BF02412215

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  • DOI: https://doi.org/10.1007/BF02412215

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