p-Laplacian type equations involving measures

Details p-Laplacian type equations involving measures p-Laplacian type equations involving measures

2003-04-24

arxiv.org/abs/math/0304392v1

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

Mathematics

Analysis of PDEs

Scientific paper

This is a survey on problems involving equations $-\operatorname{div}{\Cal A}(x,\nabla u)=\mu$, where $\mu$ is a Radon measure and ${\Cal A}:\bold {R}^n\times\bold R^n\to \bold R^n$ 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.

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