Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem

DOI10.1016/j.aim.2009.11.005zbMath1186.49031OpenAlexW2052272168MaRDI QIDQ962155

Adrian Tudorascu, Wilfrid Gangbo

Publication date: 6 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.aim.2009.11.005

zbMATH Keywords

Wasserstein metricmass transfer

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Variational problems in a geometric measure-theoretic setting (49Q20) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

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An infinite-dimensional weak KAM theory via random variables ⋮ Existence of Solutions of the Master Equation in the Smooth Case ⋮ The Aubry set for a version of the Vlasov equation ⋮ Viscous Aubry-Mather theory and the Vlasov equation ⋮ Geodesics of minimal length in the set of probability measures on graphs ⋮ Towards weak KAM theory at relative equilibrium ⋮ Homogenization for a class of integral functionals in spaces of probability measures ⋮ A time-step approximation scheme for a viscous version of the Vlasov equation ⋮ Calculus of variations in Hilbert spaces ⋮ On the minimizers of calculus of variations problems in Hilbert spaces ⋮ On Landau damping ⋮ Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems ⋮ Metric viscosity solutions of Hamilton-Jacobi equations depending on local slopes ⋮ Weak KAM Theory on the Wasserstein Torus with Multidimensional Underlying Space ⋮ A Hamilton-Jacobi PDE associated with hydrodynamic fluctuations from a nonlinear diffusion equation ⋮ Weak KAM theory for potential MFG ⋮ On the long time convergence of potential MFG

Cites Work

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• The Vlasov dynamics and its fluctuations in the \(1/N\) limit of interacting classical particles
• Hamilton-Jacobi equations in infinite dimensions. I: Uniqueness of viscosity solutions
• Vlasov equations
• Hamilton-Jacobi equations in infinite dimensions. III
• Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems
• Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems
• Hamiltonian ODEs in the Wasserstein space of probability measures

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