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

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June 2018, 13(2): 373-378. doi: 10.3934/nhm.2018016

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 September 2017 Revised October 2017 Published May 2018

Fund Project: This work was partially supported by the ANR HJnet ANR-12-BS01-0008-01 and by EU under the 7th Framework Programme Marie Curie Initial Training Network "FP7-PEOPLE-2010-ITN", SADCO project, GA number 264735-SADCO

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].

Keywords: Optimal control, discontinuous dynamic, stratified domains, Bellman equation, viscosity solutions.

Mathematics Subject Classification: Primary: 49L20, 49L25; Secondary: 35F21.

Citation: Guy Barles, Emmanuel Chasseigne. Corrigendum to "(Almost) everything you always wanted to know about deterministic control problems in stratified domains". Networks & Heterogeneous Media, 2018, 13 (2) : 373-378. doi: 10.3934/nhm.2018016

References:

[1]	G. Barles and E. Chasseigne, (Almost) Everything you always wanted to know about deterministic control problems in stratified domains, Netw. Heterog. Media, 10 (2015), 809-836. doi: 10.3934/nhm.2015.10.809.
[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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References:

[1]	G. Barles and E. Chasseigne, (Almost) Everything you always wanted to know about deterministic control problems in stratified domains, Netw. Heterog. Media, 10 (2015), 809-836. doi: 10.3934/nhm.2015.10.809.
[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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