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Pré-Publication, Document De Travail Année : 2004

Smoothing And Dispersive Estimates For 1d Schrödinger Equations With BV Coefficients And Applications

N. Burq

Résumé

We prove smoothing estimates for Schrödinger 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.

Dates et versions

hal-00017563 , version 1 (24-01-2006)

Identifiants

Citer

N. Burq, F. Planchon. Smoothing And Dispersive Estimates For 1d Schrödinger Equations With BV Coefficients And Applications. 2004. ⟨hal-00017563⟩
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