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March  2007, 6(1): 203-212. doi: 10.3934/cpaa.2007.6.203

Remarks on dispersive estimates and curvature

Fabio Nicola 1,

1. 

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received  March 2006 Revised  October 2006 Published  December 2006

We investigate connections between certain dispersive estimates of a (pseudo) differential operator of real principal type and the number of non-vanishing curvatures of its characteristic manifold. More precisely, we obtain sharp thresholds for the range of Lebesgue exponents depending on the specific geometry.
Keywords: Strichartz estimates, Dispersive estimates, Gaussian curvature..
Mathematics Subject Classification: Primary: 35S05; Secondary: 35B45, 47G3.
Citation: Fabio Nicola. Remarks on dispersive estimates and curvature. Communications on Pure & Applied Analysis, 2007, 6 (1) : 203-212. doi: 10.3934/cpaa.2007.6.203
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