TY - JOUR
T1 - A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations
AU - de la Llave, Rafael
AU - Valdinoci, Enrico
PY - 2009/1/1
Y1 - 2009/1/1
N2 - 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.
AB - 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.
KW - Aubry-Mather theory
KW - Calculus of variations
KW - Comparison
KW - Gradient flow
KW - Possibly degenerate and fractional operators
KW - Quasi-periodic solutions
KW - Subordination
UR - http://www.scopus.com/inward/record.url?scp=67649628406&partnerID=8YFLogxK
U2 - 10.1016/j.anihpc.2008.11.002
DO - 10.1016/j.anihpc.2008.11.002
M3 - Article
AN - SCOPUS:67649628406
SN - 0294-1449
VL - 26
SP - 1309
EP - 1344
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 4
ER -