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

The aim of this short note is: $(i)$ to report an error in \cite{Strat}; $(ii)$ toexplain why the comparison result of \cite{Strat} lacks an hypothesis in thedefinition of subsolutions if we allow them to be discontinuous; $(iii)$~todescribe a simple counter-example; $(iv)$ to show a simple way to c...

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Bibliographic Details
Published in:Networks and heterogeneous media 2018, Vol.13 (2), p.373-378
Main Authors: Barles, Guy, Chasseigne, Emmanuel
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
Online Access:Get full text
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Summary:The aim of this short note is: $(i)$ to report an error in \cite{Strat}; $(ii)$ toexplain why the comparison result of \cite{Strat} lacks an hypothesis in thedefinition of subsolutions if we allow them to be discontinuous; $(iii)$~todescribe a simple counter-example; $(iv)$ to show a simple way to correct thismistake, 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~\cite{Strat}.
ISSN:1556-181X
1556-1801
1556-181X
DOI:10.3934/nhm.2018016