p-Laplacian type equations involving measures

2003/04/24 by Tero Kilpeläinen
Mathematics · #math.AP #msc:35J60 #msc:31C45

paper · pdf

published as Proceedings of the ICM, Beijing 2002, vol. 3, 167--176

arxiv created 2003/04/24 · arxiv updated 2009/11/30

Abstract

This is a survey on problems involving equations -div\Cal A(x,∇ u)=μ, where μ is a Radon measure and \Cal A:\bold Rⁿ×\bold Rⁿ→ \bold Rⁿ 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.

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