2011/08/05 by Matthew Rudd, Matthew B. Rudd, Rudd, Matthew B. +2
Computer Science · Engineering · Mathematics · #35 #39B #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #math.CA #msc:35 #msc:39B
paper · pdf · doi:10.48550/arxiv.1108.1370
arxiv created 2011/08/05 · openalex publication_date 2011/08/05 · arxiv updated 2011/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the mean value property of harmonic functions, we introduce the local and global median value properties for continuous functions of two variables. We show that the Dirichlet problem associated with the local median value property is either easy or impossible to solve, and we prove that continuous functions with this property are 1-harmonic in the viscosity sense. We then close with the following conjecture: a continuous function having the global median value property and prescribed boundary values coincides with the function of least gradient having those same boundary values.