Existence of \(C^1\) critical subsolutions of the Hamilton-Jacobi equation

DOI10.1007/s00222-003-0323-6zbMath1061.58008OpenAlexW2002279673MaRDI QIDQ1879016

Antonio Siconolfi, Albert Fathi

Publication date: 22 September 2004

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-003-0323-6

zbMATH Keywords

Hamilton-Jacobi equationsLagrangian systems

Mathematics Subject Classification ID

Related Items (81)

Singularly perturbed control systems with noncompact fast variable ⋮ An entropic characterization of the flat metrics on the two torus ⋮ Asymptotic analysis for Hamilton-Jacobi-Bellman equations on Euclidean space ⋮ A necessary and sufficient condition for convergence of the Lax-Oleinik semigroup for reversible Hamiltonians on \(\mathbf{R}^{n}\) ⋮ An infinite-dimensional weak KAM theory via random variables ⋮ Lasry-Lions, Lax-Oleinik and generalized characteristics ⋮ Convergence of the solutions of the discounted equation: the discrete case ⋮ Asymptotic analysis for the eikonal equation with the dynamical boundary conditions ⋮ Representation formulas for contact type Hamilton-Jacobi equations ⋮ Generalized characteristics and Lax-Oleinik operators: global theory ⋮ Global results for eikonal Hamilton-Jacobi equations on networks ⋮ Generalized Maupertuis' principle with applications ⋮ Propagation of singularities for weak KAM solutions and barrier functions ⋮ Urysohn-type theorem under a dynamical constraint: non-compact case ⋮ Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem ⋮ Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions ⋮ On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case ⋮ Lasry-Lions regularization and a lemma of Ilmanen ⋮ Capillary-type boundary value problems of mean curvature flows with force and transport terms on a bounded domain ⋮ Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: the central role of Mather measures ⋮ Two remarks about Mañé's conjecture ⋮ Aubry sets vs. Mather sets in two degrees of freedom ⋮ Weak Liouville-Arnol'd theorems and their implications ⋮ Vanishing contact structure problem and convergence of the viscosity solutions ⋮ The convergence of Lax-Oleinik semigroup for time-periodic Lagrangian ⋮ On Littlewood's boundedness problem for relativistic oscillators with anharmonic potentials ⋮ Viscosity solutions methods for converse KAM theory ⋮ Wigner measures supported on weak KAM tori ⋮ The Mather problem for lower semicontinuous Lagrangians ⋮ On the centralizer of vector fields: criteria of triviality and genericity results ⋮ Regularity of viscosity solutions near KAM torus ⋮ Generalized motion of level sets by functions of their curvatures on Riemannian manifolds ⋮ Aubry-Mather theory for contact Hamiltonian systems ⋮ THE MATHER MEASURE AND A LARGE DEVIATION PRINCIPLE FOR THE ENTROPY PENALIZED METHOD ⋮ On Mather’s $\alpha $-function of mechanical systems ⋮ Chain recurrence, chain transitivity, Lyapunov functions and rigidity of Lagrangian submanifolds of optical hypersurfaces ⋮ Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders ⋮ Order property and modulus of continuity of weak KAM solutions ⋮ Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean \(n\) space ⋮ Regularity and variationality of solutions to Hamilton-Jacobi equations. II: Variationality, existence, uniqueness ⋮ Limit theorems for optimal mass transportation and applications to networks ⋮ Symplectic and contact properties of the Mañé critical value of the universal cover ⋮ Mather measures associated with a class of Bloch wave functions ⋮ PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians ⋮ A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians ⋮ Closing Aubry Sets II ⋮ A GEOMETRIC DEFINITION OF THE AUBRY–MATHER SET ⋮ Existence of C1,1C1,1 critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds ⋮ Some Results on Weak KAM Theory for Time-periodic Tonelli Lagrangian Systems ⋮ Negative entropy, zero temperature and Markov chains on the interval ⋮ Minimal measures, one-dimensional currents and the Monge-Kantorovich problem ⋮ On the number of Mather measures of Lagrangian systems ⋮ On the total disconnectedness of the quotient Aubry set ⋮ A Lagrangian Approach to Weakly Coupled Hamilton--Jacobi Systems ⋮ A finite dimensional linear programming approximation of Mather's variational problem ⋮ On the vanishing discount problem from the negative direction ⋮ Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative ⋮ A Hamilton-Jacobi PDE associated with hydrodynamic fluctuations from a nonlinear diffusion equation ⋮ Uniqueness and nonuniqueness of viscosity solutions to Aronsson's equation ⋮ Almost classical solutions of Hamilton-Jacobi equations ⋮ A dynamical condition for differentiability of Mather's average action ⋮ Existence and regularity of strict critical subsolutions in the stationary ergodic setting ⋮ On the Hausdorff dimension of the mather quotient ⋮ Hyperbolicity and exponential convergence of the Lax-Oleinik semigroup ⋮ Characterization of minimizable Lagrangian action functionals and a dual Mather theorem ⋮ On the integrability of Tonelli Hamiltonians ⋮ Weak KAM solutions of a discrete-time Hamilton-Jacobi equation in a minimax framework ⋮ Aubry-Mather theory for contact Hamiltonian systems. II ⋮ Generalized Cone Comparison Principle for Viscosity Solutions of the Aronsson Equation and Absolute Minimizers ⋮ A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud. ⋮ A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton–Jacobi Equations ⋮ Global Generalized Characteristics for the Dirichlet Problem for Hamilton--Jacobi Equations at a Supercritical Energy Level ⋮ Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians ⋮ On calibrated and separating sub-actions ⋮ Closing Aubry Sets I ⋮ Boundary case of equality in optimal Loewner-type inequalities ⋮ Viscosity solutions of general viscous Hamilton-Jacobi equations ⋮ Generic hyperbolicity of aubry sets on surfaces ⋮ Regularity of weak KAM solutions and Mañé's conjecture ⋮ The reconstruction problem for the Euler-Poisson system in cosmology ⋮ Generically Mañé set supports uniquely ergodic measure for residual cohomology class

This page was built for publication: Existence of \(C^1\) critical subsolutions of the Hamilton-Jacobi equation