Regularity of \(C^ 1\) solutions of the Hamilton-Jacobi equation.

DOI10.5802/afst.1059zbMath1059.37047OpenAlexW2321838087MaRDI QIDQ1890435

Albert Fathi

Publication date: 3 January 2005

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_2003_6_12_4_479_0

zbMATH Keywords

Hamilton-Jacobi equationEuler-Lagrange equationLegendre transformation

Mathematics Subject Classification ID

Related Items (12)

On the \(C^1\) and \(C^2\)-convergence to weak K.A.M. solutions ⋮ Regularity of the distance function from arbitrary closed sets ⋮ On invariant sets in Lagrangian graphs ⋮ Calibrations and laminations ⋮ Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures ⋮ Regularization by sup-inf convolutions on Riemannian manifolds: an extension of Lasry-Lions theorem to manifolds of bounded curvature ⋮ Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry ⋮ Closing Aubry Sets II ⋮ Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds ⋮ Closing Aubry Sets I ⋮ Generic hyperbolicity of aubry sets on surfaces ⋮ Tonelli Hamiltonians without conjugate points and \(C^0\) integrability

Cites Work

• Action minimizing invariant measures for positive definite Lagrangian systems
• The Hamilton-Jacobi equation. A global approach
• Hamiltonian diffeomorphisms and Lagrangian distributions
• Horospheres and the stable part of the geodesic flow
• Lipschitz regularity in some geometric problems
• Regularity classes for operations in convexity theory
• The Cauchy problem for a nonlinear first order partial differential equation
• Inégalités ``a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques. (`A priori' inequalities for Langrangian tori invariant under symplectic diffeomorphisms)
• Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens
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