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Regularization of Subsolutions in Discrete Weak KAM Theory

Published online by Cambridge University Press:  20 November 2018

Patrick Bernard  and
Maxime Zavidovique
Patrick Bernard
Affiliation:
Département de mathématiques et applications, UMR CNRS 8553, Ecole Normale Supérieure, 45 rue d'Ulm, 75005, Paris, France, e-mail: patrick.bernard@ceremade.dauphine.fr
Maxime Zavidovique
Affiliation:
Institut de mathématiques de Jussieu, UMR CNRS 8553, Université Pierre et Marie Curie, Case 247, 4, Place Jussieu, UMR CNRS 7586, Paris, France, e-mail: zavidovique@math.jussieu.fr
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Abstract

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We expose different methods of regularizations of subsolutions in the context of discrete weak $\text{KAM}$ theory that allow us 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

49C15discrete subsolutionsregularity
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 4 , 01 August 2013 , pp. 740 - 756
Copyright
Copyright © Canadian Mathematical Society 2013

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