Weak kam theorem on non compact manifolds
Weak kam theorem on non compact manifolds
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DOI：
10.1007/s00030-007-2047-6
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发表时间：
2007-10-01
影响因子：
1.2
通讯作者：
Maderna, Ezequiel
中科院分区：
文献类型：
--
作者：
Fathi, Albert;Maderna, Ezequiel
本文考虑了非紧连通流形上与时间无关的满足经典变分法通常假设的C-2停止哈密顿量。利用Lax-Oleinik半群证明了相应的Hamilton-Jacobi方程的弱KAM解或粘性解的存在性。这个证明也适用于对称性的存在。我们还研究了对称性群的顺从性的作用，以了解何时可以与哈密顿量相关联的几个临界值重合。
In this paper, we consider a time independent C-2 stop Hamiltonian, satisfying the usual hypothesis of the classical Calculus of Variations, on a non-compact connected manifold. Using the Lax-Oleinik semigroup, we give a proof of the existence of weak KAM solutions, or viscosity solutions, for the associated Hamilton-Jacobi Equation. This proof works also in presence of symmetries. We also study the role of the amenability of the group of symmetries to understand when the several critical values that can be associated with the Hamiltonian coincide.