Problems involving $p$-Laplacian type equations and measures

Kilpeläinen, Tero

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Problems involving $p$ -Laplacian type equations and measures

Tero Kilpeläinen (2002)

Mathematica Bohemica

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In this paper I discuss two questions on $p$ -Laplacian type operators: I characterize sets that are removable for Hölder continuous solutions and then discuss the problem of existence and uniqueness of solutions to $- div (| \nabla u |^{p - 2} \nabla u) = μ$ with zero boundary values; here $μ$ is a Radon measure. The joining link between the problems is the use of equations involving measures.

A regularity result for p-harmonic equations with measure data.

Menita Carozza, Antonia Passarelli di Napoli (2004)

Collectanea Mathematica

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We examine the p-harmonic equation div |grad u|. grad u = mu, where mu is a bounded Radon measure. We determine a range of p's for which solutions to the equation verify an a priori estimate. For such p's we also prove a higher integrability result.

Degenerate elliptic equations with measure data and nonlinear potentials

Tero Kilpeläinen, Jan Malý (1992)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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