Improved energy bounds for Schrödinger operators

Abstract

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.

31 pages

References in corpus (2)

• Faber-Krahn inequalities in sharp quantitative form
• Comparison results for semilinear elliptic equations using a new symmetrization method