On near optimal trajectories for a game associated with the \(\infty\)-Laplacian

DOI10.1007/s00440-010-0306-7zbMath1233.91026arXiv0812.0496OpenAlexW4300471932MaRDI QIDQ662827

Rami Atar, Amarjit Budhiraja

Publication date: 13 February 2012

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.0496

zbMATH Keywords

Bellman-Isaacs equationstochastic differential gamesinfinity-Laplaciannear saddle points

Mathematics Subject Classification ID

Differential games (aspects of game theory) (91A23) Nonlinear elliptic equations (35J60) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic games, stochastic differential games (91A15) Dynamic games (91A25)

Related Items (1)

A stochastic differential game for the inhomogeneous \(\infty \)-Laplace equation

Cites Work

• \(C^1\) regularity for infinity harmonic functions in two dimensions
• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• \(C^{1,\alpha}\) regularity for infinity harmonic functions in two dimensions
• A stochastic differential game for the inhomogeneous \(\infty \)-Laplace equation
• Another approach to the existence of value functions of stochastic differential games
• A stochastic representation for mean curvature type geometric flows
• Uniqueness of values of Aronsson operators and running costs in ``tug-of-war games
• Extension of functions satisfying Lipschitz conditions
• Multidimensional diffusion processes.
• Tug-of-war and the infinity Laplacian
• The infinity Laplacian, Aronsson's equation and their generalizations
• A deterministic‐control‐based approach motion by curvature
• A Mathematical Model in Sand Mechanics: Presentation and Analysis

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