Displaying similar documents to “Singular dynamics for semiconcave functions”

A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations

Yifeng Yu (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In Albano-Cannarsa [1] the authors proved that, under some conditions, the singularities of the semiconcave viscosity solutions of the Hamilton-Jacobi equation propagate along generalized characteristics. In this note we will provide a simple proof of this interesting result.

Singularities in contact geometry

Marc Chaperon (2003)

Banach Center Publications

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In the first half of the paper, we consider singularities of infinitesimal contact transformations and first order partial differential equations, the main results being related to the classical Sternberg-Chen theorem for hyperbolic germs of vector fields. The second half explains how to construct global generating phase functions for solutions of Hamilton-Jacobi equations and see what their singularities look like.

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness...

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...

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

Pierre Cardaliaguet (2008)

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.