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

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

min {λ k (Ω):D⊂Ω⊂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.

DOI : 10.1016/j.anihpc.2012.10.002
Classification : 49J45, 49R05, 35P15, 47A75, 35J25
Keywords: Shape optimization, Capacity, Eigenvalues, Sobolev spaces, Concentration-compactness 
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     author = {Bucur, Dorin and Buttazzo, Giuseppe and Velichkov, Bozhidar},
     title = {Spectral optimization problems with internal constraint},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {477--495},
     publisher = {Elsevier},
     volume = {30},
     number = {3},
     year = {2013},
     doi = {10.1016/j.anihpc.2012.10.002},
     zbl = {1287.49049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.10.002/}
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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

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