Singular solutions to$p$-Laplacian type equations

Tero Kilpeläinen Department of Mathematics, University of Jyväskylä

TBD mathscidoc:1701.332916

Arkiv for Matematik, 37, (2), 275-289, 1997.10
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$G$_{δ}-set of vanishing$p$-capacity is the infinity set of some$A$-superharmonic function.
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@inproceedings{tero1997singular,
  title={Singular solutions to$p$-Laplacian type equations},
  author={Tero Kilpeläinen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203556084515725},
  booktitle={Arkiv for Matematik},
  volume={37},
  number={2},
  pages={275-289},
  year={1997},
}
Tero Kilpeläinen. Singular solutions to$p$-Laplacian type equations. 1997. Vol. 37. In Arkiv for Matematik. pp.275-289. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203556084515725.
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