07-267 Rafael de la Llave, Enrico Valdinoci

A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations (533K, pdf) Nov 9, 07

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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 $\Psi$DEs 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 universal 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.

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