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arXiv · 0910.0390

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

Hitoshi Ishii
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Abstract

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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Hitoshi Ishii. 2009-10-02. Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions. https://doi.org/10.1016/j.matpur.2010.10.006

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