Stable domains for higher order elliptic operators
This paper is devoted to prove that any domain satisfying a $(\delta _0,r_0)$-capacitary condition of first order is automatically $(m,p)$-stable for all $m\geqslant 1$ and $p> 1$, and for any dimension $N\geqslant 1$. In particular, this includes regular enough domains such as $\mathscr{C}^1$-do...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.630/ |
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| author | Grosjean, Jean-François Lemenant, Antoine Mougenot, Rémy |
| author_facet | Grosjean, Jean-François Lemenant, Antoine Mougenot, Rémy |
| author_sort | Grosjean, Jean-François |
| collection | DOAJ |
| description | This paper is devoted to prove that any domain satisfying a $(\delta _0,r_0)$-capacitary condition of first order is automatically $(m,p)$-stable for all $m\geqslant 1$ and $p> 1$, and for any dimension $N\geqslant 1$. In particular, this includes regular enough domains such as $\mathscr{C}^1$-domains, Lipschitz domains, Reifenberg-flat domains, but is sufficiently weak to also include cusp points. Our result extends some of the results of Hayouni and Pierre valid only for $N=2,3$, and partially extends the results of Bucur and Zolésio for higher order operators, with a different and simpler proof. |
| format | Article |
| id | doaj-art-502d717ab25941868957925fe2e243cb |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-502d717ab25941868957925fe2e243cb2025-02-07T11:23:31ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G101189120310.5802/crmath.63010.5802/crmath.630Stable domains for higher order elliptic operatorsGrosjean, Jean-François0Lemenant, Antoine1Mougenot, Rémy 2Université de Lorraine, CNRS, IECL, F-54000 Nancy, FranceUniversité de Lorraine, CNRS, IECL, F-54000 Nancy, FranceUniversité de Lorraine, CNRS, IECL, F-54000 Nancy, FranceThis paper is devoted to prove that any domain satisfying a $(\delta _0,r_0)$-capacitary condition of first order is automatically $(m,p)$-stable for all $m\geqslant 1$ and $p> 1$, and for any dimension $N\geqslant 1$. In particular, this includes regular enough domains such as $\mathscr{C}^1$-domains, Lipschitz domains, Reifenberg-flat domains, but is sufficiently weak to also include cusp points. Our result extends some of the results of Hayouni and Pierre valid only for $N=2,3$, and partially extends the results of Bucur and Zolésio for higher order operators, with a different and simpler proof.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.630/Capacity, stable domains$\gamma _m$-convergenceMosco-convergenceshape optimisation |
| spellingShingle | Grosjean, Jean-François Lemenant, Antoine Mougenot, Rémy Stable domains for higher order elliptic operators Comptes Rendus. Mathématique Capacity, stable domains $\gamma _m$-convergence Mosco-convergence shape optimisation |
| title | Stable domains for higher order elliptic operators |
| title_full | Stable domains for higher order elliptic operators |
| title_fullStr | Stable domains for higher order elliptic operators |
| title_full_unstemmed | Stable domains for higher order elliptic operators |
| title_short | Stable domains for higher order elliptic operators |
| title_sort | stable domains for higher order elliptic operators |
| topic | Capacity, stable domains $\gamma _m$-convergence Mosco-convergence shape optimisation |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.630/ |
| work_keys_str_mv | AT grosjeanjeanfrancois stabledomainsforhigherorderellipticoperators AT lemenantantoine stabledomainsforhigherorderellipticoperators AT mougenotremy stabledomainsforhigherorderellipticoperators |