Spectral Cluster Estimates for Metrics of Sobolev Regularity
نویسنده
چکیده
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 Lp estimates for the wave equation which are shown by employing wave packet techniques.
منابع مشابه
Spectral Cluster Estimates for C
In this paper, we establish Lp norm bounds for spectral clusters on compact manifolds, under the assumption that the metric is C1,1. Precisely, we show that the Lp estimates proven by Sogge in the case of smooth metrics hold under this limited regularity assumption. It is known by examples of Smith-Sogge that such estimates fail for C1,α metrics if α < 1.
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In this paper, we establish Lp norm bounds for spectral clusters on compact manifolds, under the assumption that the metric is C1,1. Precisely, we show that the Lp estimates proven by Sogge [12] in the case of smooth metrics hold under this limited regularity assumption. It is known by examples of Smith-Sogge [11] that such estimates fail for C1,α metrics if α < 1.
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