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 Hormander multiplier theorem is showed for the eigenfunction expansion of Dirichlet Laplacian on compact manifolds with boundary.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.