- 07-267 Rafael de la Llave, Enrico Valdinoci
- A generalization of Aubry-Mather theory to partial differential
equations and pseudo-differential equations
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
with non-commutative fundamental groups.
An abstract result will be provided,
from which an
Aubry-Mather-type theory for
concrete models will be derived.