Comptes Rendus
Équations aux dérivées partielles, Théorie du contrôle
A formula for the sum of n weak ☆ closed sets in L ∞
Mohsen Zivari-Rezapour1 ; Yichen Liu2  ; Behrouz Emamizadeh3, 4
1 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
2 Department of Applied Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, China
3 Department of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo, China
4 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1635-1639.

In this note, we derive an equation which describes the closure of a particular set comprising n-valued functions. This result provides an answer to a long standing question for which the particular case n=2 had been known and used frequently in the optimal control problems.

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DOI : 10.5802/crmath.520
Classification : 26E40, 49R05
Mots clés : $n-$valued functions, formulation, weak$^\star $ closure, rearrangements, eigenvalues
Mohsen Zivari-Rezapour 1 ; Yichen Liu 2 ; Behrouz Emamizadeh 3, 4

1 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
2 Department of Applied Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, China
3 Department of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo, China
4 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $},
     journal = {Comptes Rendus. Math\'ematique},
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Mohsen Zivari-Rezapour; Yichen Liu; Behrouz Emamizadeh. A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1635-1639. doi : 10.5802/crmath.520. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.520/

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