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Smoothing and dispersive estimates for 1D Schrödinger equations with BV coefficients and applications |
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| Authors: | Nicolas Burq Fabrice Planchon |
| Institution: | a Département de mathématiques, UMR 8628 du CNRS, Bât 425 Université Paris-Sud, F-91405 Orsay, France b Institut Universitaire de France c Laboratoire Analyse, Géométrie & Applications, UMR 7539, Institut Galilée, Université Paris 13, 99 avenue J.B. Clément, F-93430 Villetaneuse, France |
| Abstract: | We prove smoothing estimates for Schrödinger equations it∂?+x∂(a(x)x∂?)=0 with a(x)∈BV, real 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∈BV to be in a sense a minimal requirement. Finally, we provide an application to sharp well-posedness for a generalized Benjamin-Ono equation. |
| Keywords: | Bounded variations Benjamin-Ono equation Dispersive estimates |
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