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- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by Springer Science+Business Media New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-015-9321-5
- Publisher site
- See Article on Publisher Site
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 $$\varepsilon $$ ε -cone condition and in the family of convex sets.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Oct 31, 2015