Mathematical Research Letters
Volume 15 (2008)
Subcritical $L^p$ bounds on spectral clusters for Lipschitz metrics
Pages: 993 – 1002
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.