Superposition in the $p$-Laplace Equation
Analysis of PDEs
2016-01-19 v1
Abstract
That a superposition of fundamental solutions to the -Laplace Equation is -superharmonic -- even in the non-linear cases -- 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 -Laplacian of the superposition.
Cite
@article{arxiv.1601.04492,
title = {Superposition in the $p$-Laplace Equation},
author = {Karl K. Brustad},
journal= {arXiv preprint arXiv:1601.04492},
year = {2016}
}
Comments
14 pages, 1 figure