arXiv:1601.04492 Abstract | arXiv Analytics

arXiv:1601.04492 [math.AP]Abstract References Reviews Resources

Superposition in the $p$-Laplace Equation

Published 2016-01-18Version 1

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.

Comments: 14 pages, 1 figure

Categories: math.AP

Keywords: laplace equation, superposition, fundamental solutions, non-linear cases, simple proof

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