English

p-Laplacian type equations involving measures

Analysis of PDEs 2007-05-23 v1

Abstract

This is a survey on problems involving equations div\CalA(x,u)=μ-\operatorname{div}{\Cal A}(x,\nabla u)=\mu, where μ\mu is a Radon measure and \CalA:Rn×RnRn{\Cal A}:\bold {R}^n\times\bold R^n\to \bold R^n verifies Leray-Lions type conditions. We shall discuss a potential theoretic approach when the measure is nonnegative. Existence and uniqueness, and different concepts of solutions are discussed for general signed measures.

Keywords

Cite

@article{arxiv.math/0304392,
  title  = {p-Laplacian type equations involving measures},
  author = {Tero Kilpeläinen},
  journal= {arXiv preprint arXiv:math/0304392},
  year   = {2007}
}