Corrigendum to ' (Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains '
| Autor: | Guy Barles, Emmanuel Chasseigne |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), ANR-12-BS01-0008,HJnet,Equations de Hamilton-Jacobi sur des structures hétérogènes et des réseaux(2012), European Project: 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO(2011), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
viscosity solutions 49L20 49L25 35F21 Mistake Stability result 01 natural sciences Deterministic control Simple (abstract algebra) Bellman equation Calculus [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Bellman Equation 0101 mathematics Mathematics Discrete mathematics discontinuous dynamic viscosity solutions AMS Class No: 49L20 49L25 Applied Mathematics General Engineering Comparison results Optimal control Computer Science Applications 35F21 010101 applied mathematics Key-words: Optimal control Viscosity (programming) |
| Zdroj: | Networks and Heterogeneous Media Networks and Heterogeneous Media, 2018, 13 (2), pp.373-378. ⟨10.3934/nhm.2018016⟩ |
| ISSN: | 1556-1801 1556-181X |
| DOI: | 10.3934/nhm.2018016⟩ |
| Popis: | The aim of this short note is: \begin{document} $(i)$ \end{document} to report an error in [ 1 ]; \begin{document} $(ii)$ \end{document} to explain why the comparison result of [ 1 ] lacks an hypothesis in the definition of subsolutions if we allow them to be discontinuous; \begin{document} $(iii)$ \end{document} to describe a simple counter-example; \begin{document} $(iv)$ \end{document} to show a simple way to correct this mistake, considering the classical Ishii's definition of viscosity solutions; \begin{document} $(v)$ \end{document} finally, to prove that this modification actually fixes the the comparison and stability results of [ 1 ]. |
| Databáze: | OpenAIRE |
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