Action potential and weak KAM solutions
Action potential and weak KAM solutions
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DOI：
10.1007/s005260100081
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发表时间：
2001-12
影响因子：
2.1
通讯作者：
G. Contreras
中科院分区：
文献类型：
--
作者：
G. Contreras
对于紧致流形上的凸超线性Lagrange算子，我们刻画了A. Fathi [9]，根据它们在每个静态类别的值和由R定义的动作电位。[14]第十四话当流形M是非紧的时，我们构造了类似于黎曼几何中Busemann函数的弱KAM解.我们构造了一个紧化的Aubry集扩展使用这些Busemann弱KAM解决方案和特征的弱KAM解决方案的集合使用此扩展的Aubry集。
For convex superlinear lagrangians on a compact manifoldMwe characterize the Peierls barrier and the weak KAM solutions of the Hamilton-Jacobi equation, as defined by A. Fathi [9], in terms of their values at each static class and the action potential defined by R. Ma né [14]. When the manifoldMis non-compact, we construct weak KAM solutions similarly to Busemann functions in riemannian geometry. We construct a compactification ofby extending the Aubry set using these Busemann weak KAM solutions and characterize the set of weak KAM solutions using this extended Aubry set.