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March  2011, 31(1): 109-118. doi: 10.3934/dcds.2011.31.109

## Strichartz estimates for Schrödinger operators with a non-smooth magnetic potential

 1 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, United States

Received  January 2010 Revised  March 2011 Published  June 2011

We prove Strichartz estimates for the absolutely continuous evolution of a Schrödinger operator $H = (i\nabla + A)^2 + V$ in $R^n$, $n \ge 3$. Both the magnetic and electric potentials are time-independent and satisfy pointwise polynomial decay bounds. The vector potential $A(x)$ is assumed to be continuous but need not possess any Sobolev regularity. This work is a refinement of previous methods, which required extra conditions on ${\rm div}\,A$ or $|\nabla|^{\frac12}A$ in order to place the first order part of the perturbation within a suitable class of pseudo-differential operators.
Citation: Michael Goldberg. Strichartz estimates for Schrödinger operators with a non-smooth magnetic potential. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 109-118. doi: 10.3934/dcds.2011.31.109
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