On the Mean Value Property for the p-Laplace equation in the plane

2014/08/31 by Peter Lindqvist, Lindqvist, Peter, Juan J. Manfredi +1
Computer Science · Mathematics · #35J62 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Dynamics and Fractals #Polynomial and algebraic computation #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1409.0241

openalex publication_date 2014/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the p-Laplace equation in the plane and prove that the mean value property holds directly for the solutions themselves. This removes the need to interpret the formula in the viscosity sense via test functions. The method is based on the hodograph representation.

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