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.
Applied Mathematics and Optimization – Springer Journals
Published: Oct 31, 2015
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