We consider spectral optimization problems of the form $$minBig{lambda_1(Omega;D): Omegasubset D, |Omega|=1Big},$$ where $D$ is a given subset of the Euclidean space $R^d$. Here $lambda_1(Omega;D)$ is the first eigenvalue of the Laplace operator $-Delta$ with Dirichlet conditions on $partialOmegacap D$ and Neumann or Robin conditions on $partialOmegacappartial D$. This reminds the classical drop problems, where the first eigenvalue replaces the perimeter functional. We prove an existence result for general shape cost functionals and we show some qualitative properties of the optimal domains.

The spectral drop problem

BUTTAZZO, GIUSEPPE;Bozhidar Velichkov
2016

Abstract

We consider spectral optimization problems of the form $$minBig{lambda_1(Omega;D): Omegasubset D, |Omega|=1Big},$$ where $D$ is a given subset of the Euclidean space $R^d$. Here $lambda_1(Omega;D)$ is the first eigenvalue of the Laplace operator $-Delta$ with Dirichlet conditions on $partialOmegacap D$ and Neumann or Robin conditions on $partialOmegacappartial D$. This reminds the classical drop problems, where the first eigenvalue replaces the perimeter functional. We prove an existence result for general shape cost functionals and we show some qualitative properties of the optimal domains.
Buttazzo, Giuseppe; Velichkov, Bozhidar
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/626273
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