Volume 23, Number 2, April-June 2017
|Page(s)||627 - 635|
|Published online||24 January 2017|
Optimal design problems for Schrödinger operators with noncompact resolvents
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
Received: 18 February 2015
Revised: 13 September 2015
Accepted: 5 February 2016
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.
Mathematics Subject Classification: 49J45 / 35J10 / 58C40 / 49R05 / 35P15
Key words: Optimal potentials / Schrödinger operators / Lieb–Thirring inequality
© EDP Sciences, SMAI 2017
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