Convergence of the naturalp-means for thep-Laplacian

DOI10.1051/cocv/2021026zbMath1479.35486OpenAlexW3133772777MaRDI QIDQ4999563

Bianca Stroffolini, Juan J. Manfredi

Publication date: 7 July 2021

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/cocv/2021026

zbMATH Keywords

Dirichlet problemHeisenberg group\(p\)-Laplaciandiscrete approximationsgeneralized viscosity solutionsasymptotic mean value propertiesnatural \(p\)-means

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Viscosity solutions to PDEs (35D40) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items

Convergence of natural \(p\)-means for the \(p\)-Laplacian in the Heisenberg group ⋮ Boundary convergence properties of \(L^p\)-averages ⋮ Variational \(p\)-harmonious functions: existence and convergence to \(p\)-harmonic functions

Cites Work

• Unnamed Item
• A dynamic programming principle with continuous solutions related to the \(p\)-Laplacian, \(1<p<\infty \).
• Tug-of-war games with varying probabilities and the normalized \(p(x)\)-Laplacian
• Solutions of nonlinear PDEs in the sense of averages
• Tug-of-war with noise: a game-theoretic view of the \(p\)-Laplacian
• On the existence and uniqueness of \(p\)-harmonious functions.
• Convergence of dynamic programming principles for the \(p\)-Laplacian
• Variational approach to the asymptotic mean-value property for the \(p\)-Laplacian on Carnot groups
• General existence of solutions to dynamic programming equations
• A natural approach to the asymptotic mean value property for the \(p\)-Laplacian
• On the characterization of \(p\)-harmonic functions on the Heisenberg group by mean value properties
• On absolutely minimizing Lipschitz extensions and PDE \(\bigtriangleup_{\infty}(u)=0\)
• On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasi-Linear Equation
• On the asymptotic mean value property for planar 𝑝-harmonic functions
• An Asymptotic Mean Value Characterization for a Class of Nonlinear Parabolic Equations Related to Tug-of-War Games
• Tug-of-war and the infinity Laplacian
• Functional Integration and Partial Differential Equations. (AM-109)
• On the definition and properties of p-superharmonic functions.
• The Dirichlet Problem for Semilinear Second-Order Degenerate Elliptic Equations and Applications to Stochastic Exit Time Control Problems
• Harmonious Extensions
• Game Theory and Partial Differential Equations