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# Regularization of Subsolutions in Discrete Weak KAM Theory

Published:2013-01-23
Printed: Aug 2013
• P. Bernard,
Université Paris-Dauphine
• M. Zavidovique,
Université Paris 6
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## Abstract

We expose different methods of regularizations of subsolutions in the context of discrete weak KAM theory. They allow to prove the existence and the density of $C^{1,1}$ subsolutions. Moreover, these subsolutions can be made strict and smooth outside of the Aubry set.
 Keywords: discrete subsolutions, regularity
 MSC Classifications: 49C15 - unknown classification 49C15