Calculus of Variations and Geometric Measure Theory

L. Brasco - G. Buttazzo

Improved energy bounds for Schrödinger operators

created by brasco on 24 Feb 2014
modified on 31 Aug 2014


Accepted Paper

Inserted: 24 feb 2014
Last Updated: 31 aug 2014

Journal: Calc. Var. Partial Differential Equations
Pages: 31
Year: 2014


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.

Keywords: stability inequalities, Schrodinger operators, Optimal potentials, decay estimates