Strichartz estimates for Schrödinger operators with a non-smooth magnetic potential
Michael Goldberg
Discrete & Continuous Dynamical Systems - A 2011, 31(1): 109-118 doi: 10.3934/dcds.2011.31.109
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.
keywords: Strichartz estimates. resolvents Magnetic Schrödinger operators local smoothing

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