# The Steklov Spectrum on Moving Domains

The Steklov Spectrum on Moving Domains 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# The Steklov Spectrum on Moving Domains

, Volume 75 (1) – Oct 31, 2015
25 pages

/lp/springer_journal/the-steklov-spectrum-on-moving-domains-E0w0FOo21I
Publisher
Springer US
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
D.O.I.
10.1007/s00245-015-9321-5
Publisher site
See Article on Publisher Site

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