Mathematical Research Letters

Volume 15 (2008)

Number 5

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

Pages: 993 – 1002

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n5.a12

Authors

Herbert Koch (Universität Bonn)

Hart F. Smith (University of Washington)

Daniel Tataru (University of California at Berkeley)

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

Full Text (PDF format)