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Global Strichartz estimates for nontrapping geometries: About an article by H. Smith and C. Sogge. (English) Zbl 1026.35020
Summary: The purpose of this note is to present an alternative proof of a result by H. Smith and C. Sogge [ibid. 25, 2171-2183 (2000; Zbl 0972.35014)] showing that in odd dimension of space, local (in time) Strichartz estimates and exponential decay of the local energy for solutions to wave equations imply global Strichartz estimates. Our proof allows to extend the result to the case of even dimensions of space.

MSC:
35B45 A priori estimates in context of PDEs
35L05 Wave equation
35B40 Asymptotic behavior of solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
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