The Steklov spectrum on moving domains. (English) Zbl 1359.49015
Summary: 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 \(\varepsilon \)-cone condition and in the family of convex sets.
MSC:
| 49Q10 | Optimization of shapes other than minimal surfaces |
| 35P15 | Estimates of eigenvalues in context of PDEs |
References:
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