Remarks on Viscosity Super-Solutions of Quasi-Variational Inequalities
Analysis of PDEs
2021-02-08 v2 Optimization and Control
Abstract
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.
Keywords
Cite
@article{arxiv.2010.12738,
title = {Remarks on Viscosity Super-Solutions of Quasi-Variational Inequalities},
author = {Yue Zhou and Xinwei Feng and Jiongmin Yong},
journal= {arXiv preprint arXiv:2010.12738},
year = {2021}
}