On the topology of the set of singularities of a solution to the Hamilton-Jacobi equation

DOI10.1016/j.crma.2016.12.004zbMath1361.35043OpenAlexW2560901311MaRDI QIDQ514388

Albert Fathi, Wei Cheng, Piermarco Cannarsa

Publication date: 1 March 2017

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2016.12.004

zbMATH Keywords

Lax-Oleinik semi-group

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) Singularity in context of PDEs (35A21) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21)

Related Items

Local strict singular characteristics: Cauchy problem with smooth initial data, Representation formulas for contact type Hamilton-Jacobi equations, Generalized characteristics and Lax-Oleinik operators: global theory, Dynamic and asymptotic behavior of singularities of certain weak KAM solutions on the torus, Global behaviors of weak KAM solutions for exact symplectic twist maps, Local strict singular characteristics. II: Existence for stationary equations on \(\mathbb{R}^2\), Herglotz' variational principle and Lax-Oleinik evolution, Towards weak KAM theory at relative equilibrium, Topology of singular set of semiconcave function via Arnaud's theorem, Propagation of singularities of Moreau envelopes and distance functions in a Hilbert space, Global structure and regularity of solutions to the Eikonal equation, Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry, 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 \(\mathbb{R}^2\), 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, Nonexistence of global characteristics for viscosity solutions

Cites Work

• Singular gradient flow of the distance function and homotopy equivalence
• Weak KAM from a PDE point of view: viscosity solutions of the Hamilton–Jacobi equation and Aubry set
• Existence of C1,1C1,1 critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds
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