Mean value property for 𝑝-harmonic functions-Reference-Cited by-同舟云学术

Mean value property for 𝑝-harmonic functions

Published:2011-11-21 Issue:7 Volume:140 Page:2453-2463
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Giorgi Tiziana,Smits Robert

Abstract

We derive a mean value property for p p -harmonic functions in two dimensions, 1 > p > ∞ 1>p>\infty , which holds asymptotically in the viscosity sense. The formula coincides with the classical mean value property for harmonic functions, when p = 2 p=2 , and is a consequence of a representation for the Game p p -Laplacian obtained via p p -averaging.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2012-140-07/S0002-9939-2011-11181-X/S0002-9939-2011-11181-X.pdf

Reference9 articles.

1. Convergence of approximation schemes for fully nonlinear second order equations;Barles, G.;Asymptotic Anal.,1991

2. W Blaschke. Ein Mittelwertsatz und eine kennzeichnende Eigenschaft des logarithmischen Potentials. Leipz. Ber. 68 (1916), 37.

3. User’s guide to viscosity solutions of second order partial differential equations;Crandall, Michael G.;Bull. Amer. Math. Soc. (N.S.),1992

4. M. Falcone, S. Finzi Vita, T. Giorgi and R. Smits. A semi-Lagrangian scheme for the Game 𝑝-Laplacian via 𝑝-averaging. Submitted.

5. On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation;Juutinen, Petri;SIAM J. Math. Anal.,2001

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