The Steklov Spectrum on Moving Domains

Beniamin Bogosel

doi:10.1007/s00245-015-9321-5

The Steklov Spectrum on Moving Domains

Beniamin Bogosel

Université Savoie Mont Blanc

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We study the continuity of the Steklov spectrum on variable domains with respect to the Hausdorff convergence. A key point of the article is understanding the behaviour of the traces of Sobolev functions on moving boundaries of sets satisfying an uniform geometric condition. As a consequence, we are able to prove existence results for shape optimization problems regarding the Steklov spectrum in the family of sets satisfying a ε-cone condition and in the family of convex sets.

langue originale	Anglais
Pages (de - à)	1-25
Nombre de pages	25
journal	Applied Mathematics & Optimization
Volume	75
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s00245-015-9321-5
état	Publié - 1 févr. 2017
Modification externe	Oui

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10.1007/s00245-015-9321-5

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title = "The Steklov Spectrum on Moving Domains",

abstract = "We study the continuity of the Steklov spectrum on variable domains with respect to the Hausdorff convergence. A key point of the article is understanding the behaviour of the traces of Sobolev functions on moving boundaries of sets satisfying an uniform geometric condition. As a consequence, we are able to prove existence results for shape optimization problems regarding the Steklov spectrum in the family of sets satisfying a ε-cone condition and in the family of convex sets.",

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KW - Steklov spectrum

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The Steklov Spectrum on Moving Domains

Résumé

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