Mathematical Research Letters

Volume 15 (2008)

Number 5

Subcritical $L^p$ bounds on spectral clusters for Lipschitz metrics

Pages: 993 – 1002



Herbert Koch (Universität Bonn)

Hart F. Smith (University of Washington)

Daniel Tataru (University of California at Berkeley)


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 $6\lt p\lt \infty$. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.

Published 1 January 2008