Subcritical Lp bounds on spectral clusters for Lipschitz metrics
Analysis of PDEs
2007-09-19 v1
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.
Cite
@article{arxiv.0709.2764,
title = {Subcritical Lp bounds on spectral clusters for Lipschitz metrics},
author = {Herbert Koch and Hart F. Smith and Daniel Tataru},
journal= {arXiv preprint arXiv:0709.2764},
year = {2007}
}
Comments
10 pages