论文标题
关于准变化不平等的粘度超溶液的评论
Remarks on Viscosity Super-Solutions of Quasi-Variational Inequalities
论文作者
论文摘要
对于Hamilton-Jacobi-Bellman（HJB）方程，具有粘度超溶液和子溶液的标准定义，众所周知，任何（粘度）超级分析和子溶液之间都有比较。对于最佳的冲动控制问题而引起的HJB类型的准变量不平等（QVI），这应该是相同的。然而，根据Barles 1985中发现的定义的自然采用，Barles 1985b，可以保证粘度解决方案的独特性，但是无法保证粘度超级和子分解之间的比较。本文介绍了HJB型QVI的粘度超溶液的定义的修改，以便将所需的比较定理保存。
For Hamilton-Jacobi-Bellman (HJB) equations, with the standard definitions of viscosity super-solution and sub-solution, it is known that there is a comparison between any (viscosity) super-solutions and sub-solutions. This should be the same for HJB type quasi-variational inequalities (QVIs) arising from optimal impulse control problems. However, according to a natural adoption of the definition found in Barles 1985, Barles 1985b, the uniqueness of the viscosity solution could be guaranteed, but the comparison between viscosity super- and sub-solutions could not be guaranteed. This paper introduces a modification of the definition for the viscosity super-solution of HJB type QVIs so that the desired comparison theorem will hold.
