C 1;1 -smoothness of constrained solutions in the calculus of variations with application to mean field games
C 1;1 -smoothness of constrained solutions in the calculus of variations with application to mean field games
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C 1;1 - 变分计算中约束解的平滑性及其应用于平均场博弈
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
P. Cardaliaguet
中科院分区：
文献类型：
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作者：
P. Cannarsa;R. Capuani;P. Cardaliaguet
给出了光滑状态约束下变分法中正则泛函最小值的必要最优性条件。在文献中，这个经典问题得到了广泛的研究。我们的结果的新颖之处在于状态约束的存在作为局部反馈进入欧拉-拉格朗日方程，这允许推导c1；1 -解的平滑性。作为应用，我们讨论了一个有约束的平均域对策问题，我们的最优性条件允许构造Lipschitz松弛解，从而改进了前两位作者的存在性结果。
We derive necessary optimality conditions for minimizers of regular functionals in the calculus of variations under smooth state constraints. In the literature, this classical problem is widely investigated. The novelty of our result lies in the fact that the presence of state constraints enters the Euler-Lagrange equations as a local feedback, which allows to derive the C 1;1 -smoothness of solutions. As an application, we discuss a constrained Mean Field Games problem, for which our optimality conditions allow to construct Lipschitz relaxed solutions, thus improving an existence result due to the first two authors.