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Optimal potentials for Schrödinger operators

Giuseppe Buttazzo; Augusto Gerolin; Berardo Ruffini; Bozhidar Velichkov — 2014

Journal de l’École polytechnique — Mathématiques

We consider the Schrödinger operator $- Δ + V (x)$ on $H_{0}^{1} (Ω)$ , where $Ω$ is a given domain of $ℝ^{d}$ . Our goal is to study some optimization problems where an optimal potential $V \geq 0$ 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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