Spectral cluster estimates for metrics of Sobolev regularity

Blair, Matthew

doi:10.1090/S0002-9947-08-04638-2

Spectral cluster estimates for metrics of Sobolev regularity
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Trans. Amer. Math. Soc. 361 (2009), 1209-1240 Request permission

Abstract:

We investigate spectral cluster estimates for compact manifolds equipped with a Riemannian metric whose regularity is determined by its inclusion in a Sobolev space of sufficiently high order. The problem is reduced to obtaining $L^p$ estimates for the wave equation which are shown by employing wave packet techniques.

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