Sharp L^p bounds on spectral clusters for Lipschitz metrics
  We establish L^p bounds on L^2 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 $6<p\leq 8$. In higher dimensions we obtain best possible bounds for a limited range of p. 
Herbert Koch, Hart Smith and Daniel Tataru
math.AP