Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter March 12, 2009

Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem

Xiangjin Xu
From the journal

Abstract

On compact Riemannian manifolds (M,g) of dimension n ≥ 2 with smooth boundary, the gradient estimates for the eigenfunctions of the Dirichlet Laplacian are proved by the maximum principle. Using the L estimates and gradient estimates, the Hörmander multiplier theorem is shown for the eigenfunction expansion of Dirichlet Laplacian on compact manifolds with boundary.

Received: 2007-09-04
Published Online: 2009-03-12
Published in Print: 2009-May

© de Gruyter 2009