Geodesic
Optimal design problems for Schrödinger operators with noncompact resolvents
Bouchitté, Guy1  ; Buttazzo, Giuseppe2 
1 Laboratoire IMATH, Université de Toulon, BP 20132, 83957 La Garde cedex, France
2 Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 627-635 Cet article a éte moissonné depuis la source Numdam

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We consider optimization problems for cost functionals which depend on the negative spectrum of Schrödinger operators of the form -Δ+V(x), where V is a potential, with prescribed compact support, which has to be determined. Under suitable assumptions the existence of an optimal potential is shown. This can be applied to interesting cases such as costs functions involving finitely many negative eigenvalues.

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DOI : 10.1051/cocv/2016009
Classification : 49J45, 35J10, 58C40, 49R05, 35P15
Keywords: Optimal potentials, Schrödinger operators, Lieb–Thirring inequality

Bouchitté, Guy 1 ; Buttazzo, Giuseppe 2

1 Laboratoire IMATH, Université de Toulon, BP 20132, 83957 La Garde cedex, France
2 Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy 
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     title = {Optimal design problems for {Schr\"odinger} operators with noncompact resolvents},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {627--635},
     year = {2017},
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Bouchitté, Guy; Buttazzo, Giuseppe. Optimal design problems for Schrödinger operators with noncompact resolvents. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 627-635. doi: 10.1051/cocv/2016009

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