Accepted Paper
Inserted: 24 feb 2014
Last Updated: 31 aug 2014
Journal: Calc. Var. Partial Differential Equations
Pages: 31
Year: 2014
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.
Keywords: stability inequalities, Schrodinger operators, Optimal potentials, decay estimates
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