Selection problems for a discount degenerate viscous Hamilton-Jacobi equation

DOI10.1016/j.aim.2016.10.032zbMath1357.35090arXiv1408.2909OpenAlexW1706053453MaRDI QIDQ728234

Hiroyoshi Mitake, Hung V. Tran

Publication date: 19 December 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.2909

zbMATH Keywords

commutation lemmaergodic problemsnonlinear adjoint methodsstochastic Mather measures

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Hamilton-Jacobi equations (35F21)

Related Items

The selection problem for some first-order stationary mean-field games, Convergence of the solutions of discounted Hamilton-Jacobi systems, Weak KAM theory for discounted Hamilton-Jacobi equations and its application, The vanishing discount problem and viscosity Mather measures. II: Boundary value problems, The ergodic limit for weak solutions of elliptic equations with Neumann boundary condition, The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. I: Linear coupling, Convergence of discrete Aubry–Mather model in the continuous limit, Selection problems of \({{\mathbb {Z}}}^2\)-periodic entropy solutions and viscosity solutions, Long time behavior of the master equation in mean field game theory, Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function, Remarks on the vanishing discount problem for infinite systems of Hamilton-Jacobi-Bellman equations, Mather measures for space-time periodic nonconvex Hamiltonians, A Selection Principle for Weak KAM Solutions via Freidlin–Wentzell Large Deviation Principle of Invariant Measures, The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. II: Nonlinear coupling, On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case, Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: the central role of Mather measures, Unnamed Item, Unnamed Item, Vanishing contact structure problem and convergence of the viscosity solutions, On Cell Problems for Nonlinear PDES and Its Application to Homogenization, The vanishing discount problem for Hamilton–Jacobi equations in the Euclidean space, The selection problem for discounted Hamilton-Jacobi equations: some non-convex cases, On uniqueness sets of additive eigenvalue problems and applications, Generalized ergodic problems: existence and uniqueness structures of solutions, Weak KAM theory for action minimizing random walks, Aubry-Mather theory for contact Hamiltonian systems. II, Vanishing discount problem and the additive eigenvalues on changing domains, The large time profile for Hamilton-Jacobi-Bellman equations

Cites Work

• Unnamed Item
• Unnamed Item
• Limit of the infinite horizon discounted Hamilton-Jacobi equation
• Adjoint methods for static Hamilton-Jacobi equations
• Transport equation and Cauchy problem for BV vector fields
• Adjoint and compensated compactness methods for Hamilton-Jacobi PDE
• Large-time behavior for obstacle problems for degenerate viscous Hamilton-Jacobi equations
• Ordinary differential equations, transport theory and Sobolev spaces
• Action minimizing invariant measures for positive definite Lagrangian systems
• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• Control of diffusion processes in \(\mathbb R^N\)
• Aubry-Mather theory and Hamilton-Jacobi equations
• The selection problem for discounted Hamilton-Jacobi equations: some non-convex cases
• PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians
• Envelopes and nonconvex Hamilton-Jacobi equations
• A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians
• Viscosity solutions of general viscous Hamilton-Jacobi equations
• Physical solutions of the Hamilton-Jacobi equation
• On the stochastic Aubry-Mather theory
• Adjoint methods for obstacle problems and weakly coupled systems of PDE
• Aubry–Mather Measures in the Nonconvex Setting
• A stochastic analogue of Aubry-Mather theory*
• Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients
• Generalized Mather problem and selection principles for viscosity solutions and mather measures
• A Uniqueness Result for Viscosity Solutions of Second Order Fully Nonlinear Partial Differential Equations
• User’s guide to viscosity solutions of second order partial differential equations
• Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens
• Generic properties and problems of minimizing measures of Lagrangian systems
• A convergence result for the ergodic problem for Hamilton–Jacobi equations with Neumann-type boundary conditions