Corrigendum to "(Almost) everything you always wanted to know about deterministic control problems in stratified domains"

Guy Barles; Emmanuel Chasseigne; Guy Barles; Emmanuel Chasseigne

doi:10.3934/nhm.2018016

Networks and Heterogeneous Media

2018, Volume 13, Issue 2: 373-378. doi: 10.3934/nhm.2018016

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Corrigendum to "(Almost) everything you always wanted to know about deterministic control problems in stratified domains"

Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350), Fédération Denis Poisson (FR CNRS 2964), Université François-Rabelais Tours, Parc de Grandmont, 37200 Tours, France

Received: 01 September 2017 Revised: 01 October 2017
Primary: 49L20, 49L25; Secondary: 35F21

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].
- Optimal control,
- discontinuous dynamic,
- stratified domains,
- Bellman equation,
- viscosity solutions
Citation: Guy Barles, Emmanuel Chasseigne. Corrigendum to '(Almost) everything you always wanted to know about deterministic control problems in stratified domains'[J]. Networks and Heterogeneous Media, 2018, 13(2): 373-378. doi: 10.3934/nhm.2018016

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Abstract

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].

References

[1]	(Almost) Everything you always wanted to know about deterministic control problems in stratified domains. Netw. Heterog. Media (2015) 10: 809-836.
[2]	A. Bressan and Y. Hong, Optimal control problems on stratified domains, Netw. Heterog. Media., 2 (2007), 313-331 (electronic) and Errata corrige: Optimal control problems on stratified domains. Netw. Heterog. Media., 8 (2013), p625. doi: 10.3934/nhm.2007.2.313

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