English

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.

Keywords

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

R2 v1 2026-06-21T09:18:35.403Z