Given a potential $V$ and the associated Schrödinger operator -Δ+$V$, 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.

Improved energy bounds for Schrödinger operators

BUTTAZZO, GIUSEPPE
2015

Abstract

Given a potential $V$ and the associated Schrödinger operator -Δ+$V$, 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.
Brasco, L.; Buttazzo, Giuseppe
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/626270
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