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arXiv · 1208.2828

Local approximation of superharmonic and superparabolic functions in nonlinear potential theory

Juha Kinnunen·Teemu Lukkari·Mikko Parviainen
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Abstract

We prove that arbitrary superharmonic functions and superparabolic functions related to the $p$-Laplace and the $p$-parabolic equations are locally obtained as limits of supersolutions with desired convergence properties of the corresponding Riesz measures. As an application we show that a family of uniformly bounded supersolutions to the $p$-parabolic equation contains a subsequence that converges to a supersolution.

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Juha Kinnunen, Teemu Lukkari, Mikko Parviainen. 2012-08-14. Local approximation of superharmonic and superparabolic functions in nonlinear potential theory. https://arxiv.org/abs/1208.2828

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