A deterministic-control-based approach to fully nonlinear parabolic and elliptic equations

DOI10.1002/cpa.20336zbMath1204.35070OpenAlexW2097117869MaRDI QIDQ3588801

Sylvia Serfaty, Robert V. Kohn

Publication date: 10 September 2010

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.20336

zbMATH Keywords

Hamilton-Jacobi-Bellman equationviscosity solutionsemidiscrete numerical schemedeterministic game

Mathematics Subject Classification ID

2-person games (91A05) Discrete-time games (91A50) Nonlinear parabolic equations (35K55) Nonlinear elliptic equations (35J60) Hamilton-Jacobi equations (35F21) PDEs in connection with control and optimization (35Q93)

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Cites Work

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• A convergent monotone difference scheme for motion of level sets by mean curvature
• Maximal and minimal solutions of an Aronsson equation: \(L^{\infty }\) variational problems versus the game theory
• Tug-of-war with noise: a game-theoretic view of the \(p\)-Laplacian
• Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media
• A billiard-based game interpretation of the Neumann problem for the curve shortening equation
• A stochastic representation for mean curvature type geometric flows
• A geometrical approach to the study of unbounded solutions of quasilinear parabolic equations
• Dynamic programming for stochastic target problems and geometric flows
• A semi-Lagrangian scheme for the curve shortening flow in codimension-2
• On the evolution governed by the infinity Laplacian
• Convergent difference schemes for nonlinear parabolic equations and mean curvature motion
• A LEVEL SET APPROACH TO SEMICONTINUOUS VISCOSITY SOLUTIONS FOR CAUCHY PROBLEMS
• EXISTENCE AND COMPARISON RESULTS FOR FULLY NONLINEAR DEGENERATE ELLIPTIC EQUATIONS WITHOUT ZEROTH-ORDER TERM1*
• A Representation Formula for the Mean Curvature Motion
• Tug-of-war and the infinity Laplacian
• A finite difference approach to the infinity Laplace equation and tug-of-war games
• Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
• Robust Control Approach to Option Pricing: A Representation Theorem and Fast Algorithm
• User’s guide to viscosity solutions of second order partial differential equations
• A strong comparison result for the bellman equation arising in stochastic exit time control problems and its applications
• A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions
• A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations
• Viscosity solutions with shocks
• A STOCHASTIC REPRESENTATION FOR THE LEVEL SET EQUATIONS
• A Morphological Scheme for Mean Curvature Motion and Applications to Anisotropic Diffusion and Motion of Level Sets
• The Level Set Method for Systems of PDEs
• The infinity Laplacian, Aronsson's equation and their generalizations
• Option pricing: A simplified approach
• A deterministic‐control‐based approach motion by curvature
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations