Improved energy bounds for Schrödinger operators

Lorenzo Brasco (1) , Giuseppe Buttazzo (2)

1 I2M - Institut de Mathématiques de Marseille
2 Dipartimento di Matematica [Pisa]

Given a potential $V$ and the associated Schrödinger operator $-\Delta+V$, we consider the problem of providing sharp upper and lower bound on the energy of the operator. It is known that if for example $V$ or $V^{-1}$ enjoys suitable summability properties, the problem has a positive answer. In this paper we show that the corresponding isoperimetric-like inequalities can be improved by means of quantitative stability estimates.

Mots clés: Schrodinger operators; optimal potentials; stability inequalities; decay estimates

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Lorenzo Brasco, Giuseppe Buttazzo. Improved energy bounds for Schrödinger operators. 2014. ⟨hal-00955139v1⟩