Calculus of Variations and Geometric Measure Theory

G. Buttazzo - A. Gerolin - B. Ruffini - B. Velichkov

Optimal Potentials for Schrödinger Operators

created by gerolin on 02 May 2013
modified by ruffini on 05 Jun 2017


Published Paper

Inserted: 2 may 2013
Last Updated: 5 jun 2017

Journal: J. Éc. polytech. Math.
Year: 2013


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 $V\geq 0$ has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.

Keywords: spectral optimization, Schrodinger operators, Optimal potentials