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

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

2008-03-31

arxiv.org/abs/0804.0034v1

Mathematics

Analysis of PDEs

12 pages

Scientific paper

We prove Strichartz estimates for the absolutely continuous evolution of a Schr\"odinger operator $H = (i\nabla + A)^2 + V$ in $\R^n$, $n > 2$. 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.

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