Rafael de la Llave, Enrico Valdinoci
A generalization of Aubry-Mather theory to partial differential 
equations and pseudo-differential equations
(533K, pdf)

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.