Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smoothing And Dispersive Estimates For 1d Schr\"odinger Equations With
  BV Coefficients And Applications   We prove smoothing estimates for Schr\"odinger equations $i\partial_t
\phi+\partial_x (a(x) \partial_x \phi) =0$ with $a(x)\in \mathrm{BV}$, the
space of functions with bounded total variation, real, positive and bounded
from below. We then bootstrap these estimates to obtain optimal Strichartz and
maximal function estimates, all of which turn out to be identical to the
constant coefficient case. We also provide counterexamples showing $a\in
\mathrm{BV}$ to be a minimal requirement. Finally, we provide an application to
sharp wellposedness for a generalized Benjamin-Ono equation.

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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn