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arXiv · 1601.04492

Superposition in the $p$-Laplace Equation

Karl K. Brustad
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Abstract

That a superposition of fundamental solutions to the $p$-Laplace Equation is $p$-superharmonic -- even in the non-linear cases $p>2$ -- has been known since M. Crandall and J. Zhang published their paper "Another Way to Say Harmonic" in 2003. We give a simple proof and extend the result by means of an explicit formula for the $p$-Laplacian of the superposition.

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Karl K. Brustad. 2016-01-18. Superposition in the $p$-Laplace Equation. https://arxiv.org/abs/1601.04492

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