On Viscosity Solutions of Certain Hamilton–Jacobi Equations: Regularity Results and Generalized Sard's Theorems

DOI10.1080/03605300701382522zbMath1134.70007OpenAlexW2016586099MaRDI QIDQ5459788

Ludovic Rifford

Publication date: 29 April 2008

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300701382522

zbMATH Keywords

singularitiessemi-concavitylocally Lipschitz hypersurface

Mathematics Subject Classification ID

Hamilton-Jacobi equations in mechanics (70H20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (19)

Sard theorems for Lipschitz functions and applications in optimization ⋮ Unique solvability of a singular stochastic control model for population management ⋮ Lasry-Lions, Lax-Oleinik and generalized characteristics ⋮ Generalized characteristics and Lax-Oleinik operators: global theory ⋮ The Morse-Sard theorem for Clarke critical values ⋮ Dynamic and asymptotic behavior of singularities of certain weak KAM solutions on the torus ⋮ Propagation of singularities for weak KAM solutions and barrier functions ⋮ Calibrations and laminations ⋮ A weak KAM approach to the periodic stationary Hartree equation ⋮ Distance functions with dense singular sets ⋮ Regularity properties of the distance functions to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry ⋮ Nonsmooth Morse-Sard theorems ⋮ Closing Aubry Sets II ⋮ Singularities of solutions of Hamilton-Jacobi equations ⋮ Local singular characteristics on \(\mathbb{R}^2\) ⋮ Schrödinger spectra and the effective Hamiltonian of weak KAM theory on the flat torus ⋮ Closing Aubry Sets I ⋮ Generic hyperbolicity of aubry sets on surfaces ⋮ Regularity of weak KAM solutions and Mañé's conjecture

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