图的Lax-Oleinik半群
The Lax-Oleinik semi-group on graphs
摘要：
考虑图上的Tonelli Lagrangian，定义了弱KAM解，它们恰好是Lax-Oleinik半群的不动点，并证明了它们的唯一性集为Aubry集，给出了一个表示公式.主要结果是Lax Oleinik半群的长时间收敛性。弱KAM解是黏性解，在[CS]中的程函型Hamilton算子的情况下，我们证明了相反的情形成立.
英文摘要：
We consider Tonelli Lagrangians on a graph, define weak KAM solutions, which happen to be the fixed points of the Lax-Oleinik semi-group, and identify their uniqueness set as the Aubry set, giving a representation formula. Our main result is the long time convergence of the Lax Oleinik semi-group. Weak KAM solutions are viscosity solutions, and in the case of Hamiltonians called of eikonal type in [CS], we prove that the converse holds.
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