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

Guy Barles; Emmanuel Chasseigne

doi:10.3934/nhm.2018016

Article Contents

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

This issue Previous Article A conservation law with multiply discontinuous flux modelling a flotation column Next Article

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

Guy Barles and
Emmanuel Chasseigne

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: August 31, 2017

Revised: September 30, 2017

Published: May 2018

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.

Abstract Full Text(HTML) Related Papers Cited by

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].

Keywords:

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

Citation:

Full Text(HTML)

Related Papers

Cited by

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.