Convergence of the semi-group of Lax–Oleinik: a geometric point of view
Convergence of the semi-group of Lax–Oleinik: a geometric point of view
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DOI：
10.1088/0951-7715/18/4/021
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发表时间：
2005-07
期刊：
影响因子：
1.7
通讯作者：
M. Arnaud
中科院分区：
文献类型：
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作者：
M. Arnaud
设M是紧致流形，是C2超线性严格凸拉格朗日算子。设是由定义的Lax-Oleinik半群，其中无穷大取于连续的和c1-分段圆弧γ：[0，t]→M使得γ(T)=x.对于c0的一个值，这个半群有不动点，并且Fathi的一个结果断言对所有人来说，一致收敛到这些不动点之一，u−.我们证明了(DTtu)图的粘附族对于Hausdorff的拓扑收敛于Du−的图的粘附族。
Let M be a compact manifold, and be a C2 superlinear and strictly convex Lagrangian. Let be the Lax–Oleinik semi-group defined by where the infinum is taken among the continuous and C1-piecewise arcs γ: [0, t] → M such that γ (t) = x. For one value of c0, this semi-group has fixed points and a result of Fathi asserts that for all , converges uniformly to one of these fixed points, u−. We prove that the family of the adherences of the graphs of (dTtu) converges for the topology of Hausdorff to the adherence of the graph of du−.