Subcritical Lp bounds on spectral clusters for Lipschitz metrics
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Subcritical Lp bounds on spectral clusters for Lipschitz metrics

  • Author(s): Koch, H
  • Smith, HF
  • Tataru, D
  • et al.
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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