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Giuseppe Buttazzo; Augusto Gerolin; Berardo Ruffini; Bozhidar Velichkov
Optimal potentials for Schrödinger operators
(Potentiels optimaux pour les opérateurs de Schrödinger)
Journal de l'École polytechnique — Mathématiques, 1 (2014), p. 71-100, doi: 10.5802/jep.4
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Class. Math.: 49J45, 35J10, 49R05, 35P15, 35J05
Keywords: Schrödinger operators, optimal potentials, spectral optimization, capacity

Résumé - Abstract

We consider the Schrödinger operator $-\Delta +V(x)$ on $H^1_0(\Omega )$, where $\Omega $ is a given domain of $\mathbb{R}^d$. Our goal is to study some optimization problems where an optimal potential $V\ge 0$ has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.

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