A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations

Rafael de la Llave, Enrico Valdinoci

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We discuss an Aubry-Mather-type theory for solutions of non-linear, possibly degenerate, elliptic PDEs and other pseudo-differential operators. We show that for certain PDEs and ΨDEs with periodic coefficients and a variational structure it is possible to find quasi-periodic solutions for all frequencies. This results also hold under a generalized definition of periodicity that makes it possible to consider problems in covers of several manifolds, including manifolds with non-commutative fundamental groups. An abstract result will be provided, from which an Aubry-Mather-type theory for concrete models will be derived.

Original languageEnglish
Pages (from-to)1309-1344
Number of pages36
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume26
Issue number4
DOIs
Publication statusPublished - 1 Jan 2009
Externally publishedYes

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