Convergence of dynamic programming principles for the \(p\)-Laplacian

DOI10.1515/acv-2019-0043zbMath1486.35235arXiv1808.10154OpenAlexW3012134449WikidataQ109746539 ScholiaQ109746539MaRDI QIDQ2119564

Mikko Parviainen, Juan J. Manfredi, Félix del Teso

Publication date: 29 March 2022

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.10154

zbMATH Keywords

Dirichlet problemapproximation\(p\)-Laplaciandynamic programming principle

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (9)

Asymptotic mean-value formulas for solutions of general second-order elliptic equations ⋮ Convergence of natural \(p\)-means for the \(p\)-Laplacian in the Heisenberg group ⋮ Evolution driven by the infinity fractional Laplacian ⋮ \(p\)-harmonic functions by way of intrinsic mean value properties ⋮ Finite difference schemes for the parabolic \(p\)-Laplace equation ⋮ Boundary convergence properties of \(L^p\)-averages ⋮ Games associated with products of eigenvalues of the Hessian ⋮ A mean value formula for the variational \(p\)-Laplacian ⋮ Convergence of the naturalp-means for thep-Laplacian

Cites Work

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• A dynamic programming principle with continuous solutions related to the \(p\)-Laplacian, \(1<p<\infty \).
• The obstacle problem for the \(p\)-Laplacian via optimal stopping of tug-of-war games
• 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
• Regularity for nonlinear stochastic games
• Finite difference methods for the infinity Laplace and \(p\)-Laplace equations
• On the existence and uniqueness of \(p\)-harmonious functions.
• General existence of solutions to dynamic programming equations
• On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasi-Linear Equation
• On the definition and properties of $p$-harmonious functions
• Tug-of-war and the infinity Laplacian
• An asymptotic mean value characterization for 𝑝-harmonic functions
• Discontinuous solutions of deterministic optimal stopping time problems
• Exit Time Problems in Optimal Control and Vanishing Viscosity Method
• The Dirichlet Problem for Semilinear Second-Order Degenerate Elliptic Equations and Applications to Stochastic Exit Time Control Problems
• Harmonious Extensions
• A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions
• Discrete approximations to the double-obstacle problem and optimal stopping of tug-of-war games

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