Spectral optimization problems with internal constraint

Dorin Bucur; Giuseppe Buttazzo; Bozhidar Velichkov

doi:10.1016/j.anihpc.2012.10.002

JournalsaihpcVol. 30, No. 3pp. 477–495

Spectral optimization problems with internal constraint

Dorin Bucur
Laboratoire de Mathématiques (LAMA), Université de Savoie, Campus Scientifique, 73376 Le-Bourget-Du-Lac, France
Giuseppe Buttazzo
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
Bozhidar Velichkov
Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy

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Abstract

We consider spectral optimization problems with internal inclusion constraints, of the form

min {λ_{k} (Ω) : D \subset Ω \subset R^{d}, ∣Ω∣ = m},

where the set D is fixed, possibly unbounded, and $λ_{k}$ is the k-th eigenvalue of the Dirichlet Laplacian on Ω. We analyze the existence of a solution and its qualitative properties, and rise some open questions.

Cite this article

Dorin Bucur, Giuseppe Buttazzo, Bozhidar Velichkov, Spectral optimization problems with internal constraint. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 3, pp. 477–495

DOI 10.1016/J.ANIHPC.2012.10.002