(ALMOST) EVERYTHING YOU ALWAYS WANTED TO KNOW ABOUT DETERMINISTIC CONTROL PROBLEMS IN STRATIFIED DOMAINS (vol 10, pg 809, 2015)

被引：1

作者：

Barles, Guy ^{[1
]}

Chasseigne, Emmanuel ^{[1
]}

机构：

[1] Univ Francois Rabelais Tours, Lab Math & Phys Theor, CNRS, UMR 7350,Federat Denis Poisson FR 2964, Parc Grandmont, F-37200 Tours, France

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2018年 / 13卷 / 02期

基金：

欧盟第七框架计划;

关键词：

Optimal control; discontinuous dynamic; stratified domains; Bellman equation; viscosity solutions;

D O I：

10.3934/nhm.2018016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this short note is: (i) to report an error in [1]; (ii) to explain why the comparison result of [1] lacks an hypothesis in the definition of subsolutions if we allow them to be discontinuous; (iii) to describe a simple counter-example; (iv) to show a simple way to correct this mistake, considering the classical Ishii's definition of viscosity solutions; (v) finally, to prove that this modification actually fixes the the comparison and stability results of [1].

引用

页码：373 / 378

页数：6