Convergence of the natural<i>p</i>-means for the<i>p</i>-Laplacian

Manfredi, Juan J.; Stroffolini, Bianca

doi:10.1051/cocv/2021026

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…Results similar to this theorem have been obtained in [9,23,25,26], based on the p-mean η ε p . In particular, this theorem was expected to hold since the average ν p enjoys all the structural assumptions, proposed in [9], for the convergence of the underlying dynamic programming principle.…”

Section: Theorem 12 (Limits Of P-harmonious Functions)supporting

confidence: 75%

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Variational p-harmonious functions: existence and convergence to p-harmonic functions

Chandra

Ishiwata

Magnanini

et al. 2021

Nonlinear Differ. Equ. Appl.

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In a recent paper, the last three authors showed that a gametheoretic p-harmonic function v is characterized by an asymptotic mean value property with respect to a kind of mean value ν r p [v](x) defined variationally on balls Br(x). In this paper, in a domain Ω ⊂ R N , N ≥ 2, we consider the operator μ ε p , acting on continuous functions on Ω, defined by the formula[v](x), where rε(x) = min[ε, dist(x, Γ)] and Γ denotes the boundary of Ω. We first derive various properties of μ ε

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Section: Theorem 12 (Limits Of P-harmonious Functions)supporting

confidence: 75%

“…The formula (1.5) is obtained by adapting [16,Theorem 3.2]. The authors in [26] also considered the smilar problems in our paper with μ ε p where they considered the Dirichlet problem corresponding to (1.2) with the same setting as in [9], which is also different from ours.…”

Section: Theorem 12 (Limits Of P-harmonious Functions)mentioning

confidence: 93%

Variational p-harmonious functions: existence and convergence to p-harmonic functions

Chandra

Ishiwata

Magnanini

et al. 2021

Nonlinear Differ. Equ. Appl.

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Boundary Convergence Properties of Lp-AVERAGES

et al. 2023

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Nonlinear asymptotic mean value characterizations of holomorphic functions

Durastanti,

Magnanini

2024

ESAIM: COCV

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Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the classical Cauchy-Riemann equations. From these asymptotic characterizations, we derive suitable asymptotic mean value properties, which are used to construct appropriate vectorial dynamical programming principles. The aim is to construct approximation schemes for the so-called contact solutions, recently introduced by N. Katzourakis, of the nonlinear systems here considered.

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Convergence of the naturalp-means for thep-Laplacian

Abstract: In this note we prove uniform convergence in Lipschitz domains of approximations to p-harmonic functions obtained using the natural p-means introduced by Ishiwata, Magnanini, and Wadade. We also consider convergence of natural means in the Heisenberg group in the case of smooth domains.

Cited by 3 publications

References 22 publications

Variational p-harmonious functions: existence and convergence to p-harmonic functions

Variational p-harmonious functions: existence and convergence to p-harmonic functions

Boundary Convergence Properties of Lp-AVERAGES

Nonlinear asymptotic mean value characterizations of holomorphic functions

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