期刊
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
卷 44, 期 12, 页码 1466-1480出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2019.1645697
关键词
Convex duality; ergodic control; infinitesimally invariant measures; viscous Hamilton-Jacobi equations
资金
- National Science Foundation [DMS-1715210]
- Army Research Office [W911NF-17-1-001]
- INSPIRE faculty fellowship
- DST-SERB grant [EMR/2016/004810]
Uniqueness of positive solutions to viscous Hamilton-Jacobi-Bellman (HJB) equations of the form , with f a coercive function and lambda a constant, in the subquadratic case, that is, , appears to be an open problem. Barles and Meireles [Comm. Partial Differential Equations 41 (2016)] show uniqueness in the case that and for some , essentially matching earlier results of Ichihara, who considered more general Hamiltonians but with better regularity for f. Without enforcing this assumption, to our knowledge, there are no results on uniqueness in the literature. In this short article, we show that the equation has a unique positive solution for any locally Lipschitz continuous, coercive f which satisfies for some positive constant kappa. Since , this assumption imposes very mild restrictions on the growth of the potential f. We also show that this solution fully characterizes optimality for the associated ergodic problem. Our method involves the study of an infinite dimensional linear program for elliptic equations for measures, and is very different from earlier approaches. It also applies to the larger class of Hamiltonians studied by Ichihara, and we show that it is well suited to provide optimality results for the associated ergodic control problem, even in a pathwise sense, and without resorting to the parabolic problem.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据