Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions

Details Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions

2009-10-02

arxiv.org/abs/0910.0390v1

Mathematics

Analysis of PDEs

39 pages, 1 figure

Scientific paper

We establish the stability under the formations of infimum and of convex combinations of subsolutions of convex Hamilton-Jacobi equations, some comparison and existence results for convex and coercive Hamilton-Jacobi equations with the Neumann type boundary condition as well as existence results for the Skorokhod problem. We define the Aubry-Mather set associated with the Neumann type boundary problem and establish some properties of the Aubry-Mather set including the existence results for the ``calibrated'' extremals for the corresponding action functional (or variational problem).

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