English

Superposition in the $p$-Laplace Equation

Analysis of PDEs 2016-01-19 v1

Abstract

That a superposition of fundamental solutions to the pp-Laplace Equation is pp-superharmonic -- even in the non-linear cases p>2p>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 pp-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

R2 v1 2026-06-22T12:31:37.756Z