Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems

被引：0
|
作者：
Diogo Aguiar Gomes
机构：
[1] Institute of Advanced Study,
[2] Princeton University,undefined
[3] Princeton,undefined
[4] NJ 08540,undefined
[5] USA (e-mail: dgomes@math.ist.utl.pt) ,undefined
[6] Universidade Tecnica Lisboa,undefined
[7] Instituto Superior Tecnico (IST),undefined
[8] Departamento de Matematica,undefined
[9] Avenida Rovisco Pais,undefined
[10] 1049-001 Lisboa,undefined
[11] Portugal ,undefined
来源：
Calculus of Variations and Partial Differential Equations | 2002年 / 14卷
关键词：
Differential Equation; Dynamical System; Partial Differential Equation; General Condition; Asymptotic Behavior;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper we apply the theory of viscosity solutions of Hamilton-Jacobi equations to understand the structure of certain Hamiltonian flows. In particular, we describe the asymptotic behavior of minimizing orbits, and prove analogs of the classical Hamilton-Jacobi integrability theory that hold under very general conditions. Then, combining partial differential equations techniques with dynamical systems ideas (Mather measures, ergodicity) we study solutions of time-independent Hamilton-Jacobi equation, namely, uniform continuity, difference quotients and non-uniqueness.
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页码：345 / 357
页数：12
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