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

被引：40
作者：
de la Llave, Rafael [2 ]
Valdinoci, Enrico [1 ]
机构：
[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy
[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 04期
基金：
美国国家科学基金会;
关键词：
Aubry-Mather theory; Quasi-periodic solutions; Calculus of variations; Comparison; Possibly degenerate and fractional operators; Subordination; Gradient flow; CAHN TYPE EQUATION; ELLIPTIC-EQUATIONS; PERIODIC MEDIA; GROUND-STATES; STATISTICAL-MECHANICS; CRITICAL-POINTS; MIXED STATES; MODEL; INTERFACES; OPERATORS;
D O I：
10.1016/j.anihpc.2008.11.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 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. (C) 2008 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：1309 / 1344
页数：36
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