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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Data di pubblicazione: | 2015 | |
Titolo: | Improved energy bounds for Schrödinger operators | |
Autori: | Brasco L; Buttazzo G | |
Rivista: | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | |
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. | |
Digital Object Identifier (DOI): | 10.1007/s00526-014-0774-1 | |
Handle: | http://hdl.handle.net/11392/2333283 | |
Appare nelle tipologie: | 03.1 Articolo su rivista |
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