Sharp L^p bounds on spectral clusters for Lipschitz metrics

2012/07/10 by Koch, Herbert, Smith, Hart, Tataru, Daniel · 1 citation
#35P15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1207.2417

Abstract

We establish L^p bounds on L² normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all p between 2 and infinity, up to logarithmic losses for 6

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