A New Kind of Lax-Oleinik Type Operator with Parameters for Time-Periodic Positive Definite Lagrangian Systems
A New Kind of Lax-Oleinik Type Operator with Parameters for Time-Periodic Positive Definite Lagrangian Systems
复制标题
DOI：
10.1007/s00220-011-1375-x
复制
发表时间：
2010-11
影响因子：
2.4
通讯作者：
中科院分区：
文献类型：
--
作者：
在本文中，我们介绍了一种新型 Lax-Oleinik 型算子，其参数与正定拉格朗日系统相关，适用于时间周期情况和时间无关情况。一方面，具有任意初始条件的新Lax-Oleinik型算子族在时间周期情况下收敛于向后弱KAM解，而Fathi和Mather表明Lax-Oleinik半群不存在这种收敛性。另一方面，在与时间无关的情况下，具有任意初始条件的新 Lax-Oleinik 类型算子族比 Lax-Oleinik 半群更快地收敛到向后弱 KAM 解。
In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the family of new Lax-Oleinik type operators with an arbitraryas initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the family of new Lax-Oleinik type operators with an arbitraryas initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.