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Convergence of the solutions of discounted Hamilton–Jacobi systems
Advances in Calculus of Variations ( IF 1.7 ) Pub Date : 2019-02-15 , DOI: 10.1515/acv-2018-0037 Andrea Davini 1 , Maxime Zavidovique 2
Advances in Calculus of Variations ( IF 1.7 ) Pub Date : 2019-02-15 , DOI: 10.1515/acv-2018-0037 Andrea Davini 1 , Maxime Zavidovique 2
Affiliation
We consider a weakly coupled system of discounted Hamilton--Jacobi equations set on a closed Riemannian manifold. We prove that the corresponding solutions converge to a specific solution of the limit system as the discount factor goes to zero. The analysis is based on a generalization of the theory of Mather minimizing measures for Hamilton--Jacobi systems and on suitable random representation formulae for the discounted solutions.
中文翻译:
贴现 Hamilton-Jacobi 系统解的收敛性
我们考虑在闭合黎曼流形上设置的贴现哈密顿-雅可比方程的弱耦合系统。我们证明,当贴现因子变为零时,相应的解会收敛到极限系统的特定解。该分析基于对 Hamilton--Jacobi 系统的 Mather 最小化测度理论的概括以及贴现解的合适随机表示公式。
更新日期:2019-02-15
中文翻译:
贴现 Hamilton-Jacobi 系统解的收敛性
我们考虑在闭合黎曼流形上设置的贴现哈密顿-雅可比方程的弱耦合系统。我们证明,当贴现因子变为零时,相应的解会收敛到极限系统的特定解。该分析基于对 Hamilton--Jacobi 系统的 Mather 最小化测度理论的概括以及贴现解的合适随机表示公式。