Displaying similar documents to “Regularity of weak KAM solutions and Mañé’s Conjecture”

A critical point result for non-differentiable indefinite functionals

Salvatore A. Marano, Dumitru Motreanu (2004)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, two deformation lemmas concerning a family of indefinite, non necessarily continuously differentiable functionals are proved. A critical point theorem, which extends the classical result of Benci-Rabinowitz [14, Theorem 5.29] to the above-mentioned setting, is then deduced.

Viscosity solutions of the Bellman equation for exit time optimal control problems with non-Lipschitz dynamics

Michael Malisoff (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the Bellman equation for undiscounted exit time optimal control problems with fully nonlinear lagrangians and fully nonlinear dynamics using the dynamic programming approach. We allow problems whose non-Lipschitz dynamics admit more than one solution trajectory for some choices of open loop controls and initial positions. We prove a uniqueness theorem which characterizes the value functions of these problems as the unique viscosity solutions of the corresponding Bellman equations...

A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable

Pierre Cardaliaguet (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the hamiltonian. The proof relies on a reverse Hölder inequality.

Viscosity solutions methods for converse KAM theory

Diogo A. Gomes, Adam Oberman (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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The main objective of this paper is to prove new necessary conditions to the existence of KAM tori. To do so, we develop a set of explicit estimates for smooth solutions of Hamilton-Jacobi equations, using a combination of methods from viscosity solutions, KAM and Aubry-Mather theories. These estimates are valid in any space dimension, and can be checked numerically to detect gaps between KAM tori and Aubry-Mather sets. We apply these results to detect non-integrable regions in ...