# American Institute of Mathematical Sciences

January  2020, 19(1): 609-640. doi: 10.3934/cpaa.2020029

## On large potential perturbations of the Schrödinger, wave and Klein–Gordon equations

 Dipartimento di Matematica, Sapienza Università di Roma, Piero D'Ancona, Piazzale A. Moro 2, 00185 Roma, Italy

Received  November 2018 Revised  February 2019 Published  July 2019

We prove a sharp resolvent estimate in scale invariant norms of Amgon–Hörmander type for a magnetic Schrödinger operator on
 $\mathbb{R}^{n}$
,
 $n\ge3$
 $\begin{equation*} L = -(\partial+iA)^{2}+V \end{equation*}$
with large potentials
 $A, V$
of almost critical decay and regularity.
The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schrödinger, wave and Klein–Gordon flows associated to
 $L$
.
Citation: P. D'Ancona. On large potential perturbations of the Schrödinger, wave and Klein–Gordon equations. Communications on Pure & Applied Analysis, 2020, 19 (1) : 609-640. doi: 10.3934/cpaa.2020029
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