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arXiv · 1402.5865

Improved energy bounds for Schr\"odinger operators

Lorenzo Brasco·Giuseppe Buttazzo
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Abstract

Given a potential $V$ and the associated Schr\"odinger 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.

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Lorenzo Brasco, Giuseppe Buttazzo. 2014-02-24. Improved energy bounds for Schr\"odinger operators. https://arxiv.org/abs/1402.5865

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