Generalized characteristics and Lax-Oleinik operators: global theory

DOI10.1007/s00526-017-1219-4zbMath1378.35078arXiv1605.07581OpenAlexW2963732948MaRDI QIDQ1674608

Wei Cheng, Piermarco Cannarsa

Publication date: 25 October 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.07581

zbMATH Keywords

generalized characteristicsautonomous Tonelli systemssup-convolutions

Mathematics Subject Classification ID

Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Singularity in context of PDEs (35A21) Hamilton-Jacobi equations (35F21)

Related Items (max. 100)

Local strict singular characteristics: Cauchy problem with smooth initial data ⋮ Representation formulas for contact type Hamilton-Jacobi equations ⋮ Dynamic and asymptotic behavior of singularities of certain weak KAM solutions on the torus ⋮ Local strict singular characteristics. II: Existence for stationary equations on \(\mathbb{R}^2\) ⋮ Herglotz' variational principle and Lax-Oleinik evolution ⋮ Topology of singular set of semiconcave function via Arnaud's theorem ⋮ Propagation of singularities of Moreau envelopes and distance functions in a Hilbert space ⋮ Lasry-Lions approximations for discounted Hamilton-Jacobi equations ⋮ Generation of singularities from the initial datum for Hamilton-Jacobi equations ⋮ Singularities of solutions of Hamilton-Jacobi equations ⋮ Local singular characteristics on \(\mathbb{R}^2\) ⋮ The distance function in the presence of an obstacle ⋮ Global Generalized Characteristics for the Dirichlet Problem for Hamilton--Jacobi Equations at a Supercritical Energy Level ⋮ Global propagation of singularities for discounted Hamilton-Jacobi equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global propagation of singularities for time dependent Hamilton-Jacobi equations
• Lasry-Lions, Lax-Oleinik and generalized characteristics
• Propagation of singularities for weak KAM solutions and barrier functions
• On the topology of the set of singularities of a solution to the Hamilton-Jacobi equation
• Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Global propagation of singularities for solutions of Hamilton-Jacobi equations
• Excess action and broken characteristics for Hamilton-Jacobi equations
• Singular dynamics for semiconcave functions
• Propagation of singularities for solutions of Hamilton-Jacobi equations
• Action minimizing invariant measures for positive definite Lagrangian systems
• A remark on regularization in Hilbert spaces
• Variational construction of connecting orbits
• Autonomous integral functionals with discontinuous nonconvex integrands: Lipschitz regularity of minimizers, BuBois-Reymond necessary conditions, and Hamilton-Jacobi equations
• Propagation of singularities for solutions of nonlinear first order partial differential equations
• Existence of \(C^1\) critical subsolutions of the Hamilton-Jacobi equation
• Singular gradient flow of the distance function and homotopy equivalence
• Uniform hyperbolicity of invariant cylinder
• Weak KAM theorem on non compact manifolds
• The regularity of the distance function propagates along minimizing geodesics
• The Lax–Oleinik semi-group: a Hamiltonian point of view
• The Principle of Least Action and Fundamental Solutions of Mass-Spring and N-Body Two-Point Boundary Value Problems
• The dynamics of pseudographs in convex Hamiltonian systems
• Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens
• Homoclinic orbits and critical points of barrier functions
• Existence of C1,1C1,1 critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds
• On Viscosity Solutions of Certain Hamilton–Jacobi Equations: Regularity Results and Generalized Sard's Theorems
• Optimal Transport
• On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations

This page was built for publication: Generalized characteristics and Lax-Oleinik operators: global theory