Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. V: Unbounded linear terms and \(B\)-continuous solutions

DOI10.1016/0022-1236(91)90010-3zbMath0739.49017OpenAlexW1978169712MaRDI QIDQ1175016

Michael G. Crandall, Pierre-Louis Lions

Publication date: 25 June 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(91)90010-3

zbMATH Keywords

Fréchet differentialinfinite dimensionsfirst order Hamilton-Jacobi equations\(B\)-continuityreal separable infinite dimensional Hilbert spaceunbounded linear maximal monotone operator

Mathematics Subject Classification ID

Related Items (34)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Interior a priori estimates for solutions of fully nonlinear equations
• Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order
• Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations
• Perron's method for Hamilton-Jacobi equations
• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• Remarques sur des résultats d'existence pour les équations de Hamilton-Jacobi du premier ordre
• Existence results for first order Hamilton Jacobi equations
• On the Hamilton-Jacobi-Bellmann equations in Banach spaces
• The necessary conditions for optimal control in Hilbert spaces
• Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations
• Optimization of functions on certain subsets of Banach spaces
• Application of viscosity solutions of infinite-dimensional Hamilton- Jacobi-Bellman equations to some problems in distributed optimal control
• Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III: Uniqueness of viscosity solutions for general second-order equations
• Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. I: The case of bounded stochastic evolutions
• Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. IV: Hamiltonians with unbounded linear terms
• Max-min representations and product formulas for the viscosity solutions of Hamilton-Jacobi equations with applications to differential games
• Optimal control of diffusion processes and hamilton–jacobi–bellman equations part 2 : viscosity solutions and uniqueness
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• Viscosity Solutions of Hamilton-Jacobi Equations
• On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's
• Hölder gradient estimates for fully nonlinear elliptic equations
• A Uniqueness Result for Viscosity Solutions of Second Order Fully Nonlinear Partial Differential Equations
• Nonconvex minimization problems
• Representation of solutions of Hamilton-Jacobi equations

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