Homogenization of Hamilton-Jacobi equations   in Carnot Groups

Bianca Stroffolini

Displaying similar documents to “Homogenization of Hamilton-Jacobi equations in Carnot Groups”

Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations

Alessandra Cutrì, Francesca Da Lio (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form $u_{t} + H (x, D u) = 0$ in $I R^{n} \times (0, T)$ where the Hamiltonian may be noncoercive in the gradient As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.

A Hamilton-Jacobi approach to junction problems and application to traffic flows

Cyril Imbert, Régis Monneau, Hasnaa Zidani (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a “junction”, that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to...

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 ...

Existence results for first order Hamilton Jacobi equations

G. Barles (1984)

Annales de l'I.H.P. Analyse non linéaire

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GO++: A modular Lagrangian/Eulerian software for Hamilton Jacobi equations of geometric optics type

Jean-David Benamou, Philippe Hoch (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.

An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces

Piermarco Cannarsa, Giuseppe Da Prato (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.

Optimal control problems with upper semicontinuous Hamiltonians

Arkadiusz Misztela (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to introduce approximate solutions of equations with such type Hamiltonians. We show that the value...