, Volume 37, Issue 2, pp 275-289

Singular solutions top-Laplacian type equations

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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.

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