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arXiv · 0709.2764

Subcritical Lp bounds on spectral clusters for Lipschitz metrics

Herbert Koch·Hart F. Smith·Daniel Tataru
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Abstract

We establish asymptotic bounds on the L^p norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range p>6. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.

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Herbert Koch, Hart F. Smith, Daniel Tataru. 2007-09-18. Subcritical Lp bounds on spectral clusters for Lipschitz metrics. https://arxiv.org/abs/0709.2764

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