no. 2
Biharmonic Steklov operator on differential forms
[Opérateur de Steklov biharmonique sur les formes différentielles]
Fida El Chami1 ; Nicolas Ginoux2 ; Georges Habib3 ; Ola Makhoul1
1 Lebanese University, Faculty of Sciences II, Department of Mathematics, P.O. Box 90656 Fanar-Matn Lebanon
2 Université de Lorraine, CNRS, IECL, 57000 Metz, France
3 Lebanese University, Faculty of Sciences II, Department of Mathematics, P.O. Box 90656 Fanar-Matn Lebanon Université de Lorraine, CNRS, IECL, 57000 Metz, France
Annales mathématiques Blaise Pascal, Tome 31 (2024) no. 2, pp. 189-237.

Nous introduisons le problème de Steklov biharmonique sur les formes différentielles en considérant des conditions de bord adaptées. Nous caractérisons sa plus petite valeur propre et établissons des propriétés élémentaires de son spectre. Nous obtenons des estimations diverses de la première valeur propre, dont certaines font intervenir des valeurs propres d’autres problèmes tels que ceux de Dirichlet, de Neumann, de Robin et de Steklov. Indépendamment, nous montrons de nouvelles inégalités reliant les valeurs propres de ces derniers problèmes.

We introduce the biharmonic Steklov problem on differential forms by considering suitable boundary conditions. We characterize its smallest eigenvalue and prove elementary properties of the spectrum. We obtain various estimates for the first eigenvalue, some of which involve eigenvalues of other problems such as the Dirichlet, Neumann, Robin and Steklov ones. Independently, new inequalities relating the eigenvalues of the latter problems are proved.

Publié le :
DOI : 10.5802/ambp.429
Classification : 53C21, 58J32, 58C40, 58J50
Keywords: Manifolds with boundary, Steklov operator, biharmonic boundary value problem, Robin boundary value problem, eigenvalue estimates
Mots-clés : Variétés à bord, opérateur de Steklov, problème à bord biharmonique, problème à bord de Robin, estimations de valeurs propres

Fida El Chami 1 ; Nicolas Ginoux 2 ; Georges Habib 3 ; Ola Makhoul 1

1 Lebanese University, Faculty of Sciences II, Department of Mathematics, P.O. Box 90656 Fanar-Matn Lebanon
2 Université de Lorraine, CNRS, IECL, 57000 Metz, France
3 Lebanese University, Faculty of Sciences II, Department of Mathematics, P.O. Box 90656 Fanar-Matn Lebanon Université de Lorraine, CNRS, IECL, 57000 Metz, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Biharmonic {Steklov} operator on differential forms},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {189--237},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
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Fida El Chami; Nicolas Ginoux; Georges Habib; Ola Makhoul. Biharmonic Steklov operator on differential forms. Annales mathématiques Blaise Pascal, Tome 31 (2024) no. 2, pp. 189-237. doi : 10.5802/ambp.429. https://ambp.centre-mersenne.org/articles/10.5802/ambp.429/

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