Subcritical Lp bounds on spectral clusters for Lipschitz metrics

Details Subcritical Lp bounds on spectral clusters for Lipschitz metrics Subcritical Lp bounds on spectral clusters for Lipschitz metrics

2007-09-18

arxiv.org/abs/0709.2764v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

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.

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