Displaying similar documents to “Prolongation of classical solutions and singularities of generalized solutions”

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.