Asymptotic statistical characterizations of \(p\)-harmonic functions of two variables

DOI10.1216/RMJ-2011-41-2-493zbMath1222.31001arXiv1108.1982MaRDI QIDQ533526

Matthew Rudd, David A. Hartenstine

Publication date: 3 May 2011

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.1982

zbMATH Keywords

viscosity solutions\(p\)-harmonic functionsmean-value property

Mathematics Subject Classification ID

Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (8)

A natural approach to the asymptotic mean value property for the \(p\)-Laplacian ⋮ Nonlocal averages in space and time given by medians and the mean curvature flow ⋮ Variational approach to the asymptotic mean-value property for the \(p\)-Laplacian on Carnot groups ⋮ NONLINEAR MEAN-VALUE FORMULAS ON FRACTAL SETS ⋮ Estimates for nonlinear harmonic measures on trees ⋮ Dirichlet-to-Neumann maps on trees ⋮ Mean value properties of fractional second order operators ⋮ Statistical exponential formulas for homogeneous diffusion

Cites Work

• A convergent monotone difference scheme for motion of level sets by mean curvature
• On generalized subharmonic functions
• Subfunctions and the Dirichlet problem
• Subfunctions of several variables
• On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasi-Linear Equation
• An asymptotic mean value characterization for 𝑝-harmonic functions
• On Generalized and Viscosity Solutions of Nonlinear Elliptic Equations
• A Morphological Scheme for Mean Curvature Motion and Applications to Anisotropic Diffusion and Motion of Level Sets
• Convolution-Generated Motion and Generalized Huygens' Principles for Interface Motion
• A deterministic‐control‐based approach motion by curvature
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