Sur la convergence du semi-groupe de Lax-Oleinik

DOI10.1016/S0764-4442(98)80144-4zbMath1052.37514OpenAlexW2055173039MaRDI QIDQ4223225

Albert Fathi

Publication date: 1 March 2000

Published in: Comptes Rendus de l'Académie des Sciences - Series I - Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0764-4442(98)80144-4

Mathematics Subject Classification ID

Related Items (90)

Long-time asymptotic solutions of convex Hamilton-Jacobi equations depending on unknown functions ⋮ The selection problem for some first-order stationary mean-field games ⋮ Random Lax-Oleinik semigroups for Hamilton-Jacobi systems ⋮ Large time behavior of solutions for a class of time-dependent Hamilton-Jacobi equations ⋮ Fast weak–KAM integrators for separable Hamiltonian systems ⋮ On the \(C^1\) and \(C^2\)-convergence to weak K.A.M. solutions ⋮ A necessary and sufficient condition for convergence of the Lax-Oleinik semigroup for reversible Hamiltonians on \(\mathbf{R}^{n}\) ⋮ An infinite-dimensional weak KAM theory via random variables ⋮ Weak KAM theory for Hamilton-Jacobi equations depending on unknown functions ⋮ Weak KAM theorem for Hamilton‐Jacobi equations with Neumann boundary conditions on noncompact manifolds ⋮ Tauberian theorem for value functions ⋮ Asymptotic solutions of Hamilton-Jacobi equations with state constraints ⋮ A uniform Tauberian theorem in dynamic games ⋮ A dynamical approach to the large-time behavior of solutions to weakly coupled systems of Hamilton-Jacobi equations ⋮ The Lax-Oleinik semigroup on graphs ⋮ Large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations ⋮ Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions ⋮ A Selection Principle for Weak KAM Solutions via Freidlin–Wentzell Large Deviation Principle of Invariant Measures ⋮ Lax–Oleinik Formula on Networks ⋮ Towards weak KAM theory at relative equilibrium ⋮ Optimal control on graphs: existence, uniqueness, and long-term behavior ⋮ Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems ⋮ Coupling by reflection for controlled diffusion processes: turnpike property and large time behavior of Hamilton-Jacobi-Bellman equations ⋮ Lipschitz sub-actions for locally maximal hyperbolic sets of a \(C^1\) map ⋮ Exponential convergence to time-periodic viscosity solutions in time-periodic Hamilton-Jacobi equations ⋮ Long-time behavior of stochastic Hamilton-Jacobi equations ⋮ On commuting Tonelli Hamiltonians: autonomous case ⋮ Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions ⋮ Unnamed Item ⋮ Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms ⋮ The convergence of Lax-Oleinik semigroup for time-periodic Lagrangian ⋮ Applications of variable discounting dynamic programming to iterated function systems and related problems ⋮ The asymptotic bounds of viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations ⋮ Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton-Jacobi equations with noncoercive Hamiltonians ⋮ Viscosity solutions methods for converse KAM theory ⋮ A PDE Approach to Large-Time Asymptotics for Boundary-Value Problems for Nonconvex Hamilton–Jacobi Equations ⋮ Stable norms of non-orientable surfaces ⋮ A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems ⋮ Aubry-Mather theory for contact Hamiltonian systems ⋮ A new PDE approach to the large time asymptotics of solutions of Hamilton–Jacobi equations ⋮ Large time behavior of solutions to parabolic equations with Neumann boundary conditions ⋮ Singular Neumann problems and large-time behavior of solutions of noncoercive Hamilton-Jacobi equations ⋮ Homogenization of first-order equations with \((u/\varepsilon)\)-periodic Hamiltonians. I: Local equations ⋮ Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations ⋮ The selection problem for discounted Hamilton-Jacobi equations: some non-convex cases ⋮ One-dimensional forward-forward mean-field games ⋮ Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations ⋮ Some results on the large-time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations ⋮ Large time behavior for some nonlinear degenerate parabolic equations ⋮ Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean \(n\) space ⋮ Error estimates for the approximation of the effective Hamiltonian ⋮ PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians ⋮ A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians ⋮ The rate of convergence of the Lax-Oleinik semigroup-degenerate fixed point case ⋮ Schrödinger operators with magnetic fields and minimal action functionals ⋮ Homogenization results for a deterministic multi-domains periodic control problem ⋮ Some Results on Weak KAM Theory for Time-periodic Tonelli Lagrangian Systems ⋮ An approximation scheme for the effective Hamiltonian and applications ⋮ On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions ⋮ On uniqueness sets of additive eigenvalue problems and applications ⋮ Stability properties and large time behavior of viscosity solutions of Hamilton–Jacobi equations on metric spaces ⋮ Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative ⋮ Weak KAM theory for potential MFG ⋮ Asymptotics of values in dynamic games on large intervals ⋮ Large time behavior of solutions of Hamilton-Jacobi equations with periodic boundary data ⋮ On almost periodic viscosity solutions to Hamilton-Jacobi equations ⋮ Hyperbolicity and exponential convergence of the Lax-Oleinik semigroup ⋮ Singularities of solutions of Hamilton-Jacobi equations ⋮ Weak KAM theory for action minimizing random walks ⋮ Large-time behavior for obstacle problems for degenerate viscous Hamilton-Jacobi equations ⋮ Asymptotic solution and effective Hamiltonian of a Hamilton-Jacobi equation in the modeling of traffic flow on a homogeneous signalized road ⋮ On Aubry sets and Mather's action functional ⋮ A Survey of partial differential equations methods in weak KAM theory ⋮ Asymptotic Solutions of Viscous Hamilton–Jacobi Equations with Ornstein–Uhlenbeck Operator ⋮ On the long time convergence of potential MFG ⋮ Weak KAM solutions of a discrete-time Hamilton-Jacobi equation in a minimax framework ⋮ Twisted Lax–Oleinik formulas and weakly coupled systems of Hamilton–Jacobi equations ⋮ Ergodic optimization in dynamical systems ⋮ A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton–Jacobi Equations ⋮ Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians ⋮ Closing Aubry Sets I ⋮ Convergence of solutions for some degenerate discounted Hamilton-Jacobi equations ⋮ Long-time behavior of solutions to Hamilton-Jacobi equations with quadratic gradient term ⋮ The large time profile for Hamilton-Jacobi-Bellman equations ⋮ On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions ⋮ Failure of convergence of the Lax-Oleinik semi-group in the time periodic case ⋮ Connecting orbits of time dependent Lagrangian systems ⋮ Regularity theory for Hamilton--Jacobi equations ⋮ Symplectic homogenization ⋮ Regularity of weak KAM solutions and Mañé's conjecture

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