Arkiv för Matematik

  • Ark. Mat.
  • Volume 37, Number 2 (1999), 275-289.

Singular solutions to p-Laplacian type equations

Tero Kilpeläinen

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We construct singular solutions to equations $div\mathcal{A}(x,\nabla u) = 0,$ similar to the p-Laplacian, that tend to ∞ on a given closed set of p-capacity zero. Moreover, we show that every Gδ-set of vanishing p-capacity is the infinity set of some A-superharmonic function.


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

Article information

Ark. Mat., Volume 37, Number 2 (1999), 275-289.

Received: 13 October 1997
First available in Project Euclid: 31 January 2017

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1999 © Institut Mittag-Leffler


Kilpeläinen, Tero. Singular solutions to p -Laplacian type equations. Ark. Mat. 37 (1999), no. 2, 275--289. doi:10.1007/BF02412215.

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