Spectral optimization problems with internal constraint
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 477-495.

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

min {λ k (Ω):DΩ 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.

DOI : 10.1016/j.anihpc.2012.10.002
Classification : 49J45, 49R05, 35P15, 47A75, 35J25
Mots clés : Shape optimization, Capacity, Eigenvalues, Sobolev spaces, Concentration-compactness
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     title = {Spectral optimization problems with internal constraint},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {477--495},
     publisher = {Elsevier},
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     number = {3},
     year = {2013},
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     zbl = {1287.49049},
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Bucur, Dorin; Buttazzo, Giuseppe; Velichkov, Bozhidar. Spectral optimization problems with internal constraint. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 477-495. doi : 10.1016/j.anihpc.2012.10.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2012.10.002/

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