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Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem
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Xiangjin Xu
Veröffentlicht/Copyright:
12. März 2009
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
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Artikel in diesem Heft
- On the classification of infinite-dimensional irreducible Hermitian-symmetric affine coadjoint orbits
- A partial generalization of the Helgason Conjecture to general bounded homogeneous domains
- Antisymmetric elements in group rings with an orientation morphism
- Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem
- On loops rich in automorphisms that are abelian modulo the nucleus
- Minimal number of periodic points for C1 self-maps of compact simply-connected manifolds
- On a question of Bombieri and Bourgain
- Separate real analyticity and CR extendibility
- Coverings of Banach spaces: beyond the Corson theorem
- Genus 2 curves that admit a degree 5 map to an elliptic curve
