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arXiv · 1211.1245

Aubry sets for weakly coupled systems of Hamilton--Jacobi equations

Andrea Davini·Maxime Zavidovique
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Abstract

We introduce a notion of Aubry set for weakly coupled systems of Hamilton--Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of globally strict critical subsolutions concentrates. As in the case of a single equation, we prove the existence of critical subsolutions which are strict and smooth outside the Aubry set. This allows us to derive in a simple way a comparison result among critical sub and supersolutions with respect to their boundary data on the Aubry set, showing in particular that the latter is a uniqueness set for the critical system. We also highlight some rigidity phenomena taking place on the Aubry set.

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Andrea Davini, Maxime Zavidovique. 2012-11-06. Aubry sets for weakly coupled systems of Hamilton--Jacobi equations. https://doi.org/10.1137/120899960

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