Displaying similar documents to “Some results regarding an equation of Hamilton-Jacobi type”

Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)

Marcin Moszyński (2009)

Studia Mathematica

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We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning...

Homogenization of Hamilton-Jacobi equations in Carnot Groups

Bianca Stroffolini (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study an homogenization problem for Hamilton-Jacobi equations in the geometry of Carnot Groups. The tiling and the corresponding notion of periodicity are compatible with the dilatations of the Group and use the Lie bracket generating property.

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 ...