Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of $\protect \mathbb{R}^2$

Aissa Aibèche; Cherif Amrouche; Bassem Bahouli

doi:10.5802/crmath.407

Equations aux dérivées partielles

Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of

ℝ^{2}

Aissa Aibèche ¹ ; Cherif Amrouche ² ; Bassem Bahouli ^2,³

¹ Laboratoire de Mathématiques Appliquées, Université Ferhat Abbas, Sétif 1, Campus El Bez, 19137 Sétif, Algeria.
² Laboratoire de Mathématiques et leurs Applications, Université de Pau et des Pays de l’Adour, Avenue de l’Université, 64000 Pau, France.
³ Laboratoire des Équations aux Dérivées Partielles Non Linéaires et Histoire des Mathématiques (EDPNL-HM), ENS Kouba, 16309 Alger, Algeria.

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 587-597.

Résumé
Abstract

On donne, d’abord, deux nouvelles applications relatives à la caractérisation de l’image de l’opérateur trace dans $H^{2} (Ω)$ . Après cela, on caractérise l’image de l’opérateur trace dans les espaces de Sobolev $W^{3, p} (Ω)$ , $Ω$ étant un domaine borné, connexe de $ℝ^{2}$ de frontière lipschitzienne.

We give, first, two new applications related to the range characterization of the range of trace operator in $H^{2} (Ω)$ . After this, we characterize the range of trace operator in the Sobolev spaces $W^{3, p} (Ω)$ when $Ω$ is a connected bounded domain $ℝ^{2}$ with Lipschitz-continuous boundary.

Reçu le : 2021-10-11
Accepté le : 2022-07-16
Publié le : 2023-03-02

DOI : 10.5802/crmath.407

Affiliations des auteurs :

Aissa Aibèche ¹ ; Cherif Amrouche ² ; Bassem Bahouli ^{2, 3}

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Aissa Aib\`eche and Cherif Amrouche and Bassem Bahouli},
     title = {Trace {Operator{\textquoteright}s} {Range} {Characterization} for {Sobolev} {Spaces} on {Lipschitz} {Domains} of $\protect \mathbb{R}^2$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {587--597},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.407},
     language = {en},
}

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Aissa Aibèche; Cherif Amrouche; Bassem Bahouli. Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of $\protect \mathbb{R}^2$. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 587-597. doi : 10.5802/crmath.407. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.407/

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