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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Applied Mathematics & Optimization
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s00245-015-9321-5
Publication status	Published - 1 Feb 2017
Externally published	Yes

Keywords

Eigenvalues
Shape optimization
Steklov spectrum

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10.1007/s00245-015-9321-5

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The Steklov Spectrum on Moving Domains

Abstract

Keywords

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