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

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.
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  • 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].

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

    Citation:

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  • [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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