Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem
Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem
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DOI：
10.1515/forum.2009.021
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发表时间：
2009
影响因子：
3.8
通讯作者：
Xiangjin Xu
中科院分区：
文献类型：
--
作者：
Xiangjin Xu
在具有光滑边界的n ≥ 2维紧致黎曼流形（M，g）上，利用极大值原理证明了Dirichlet Laplacian特征函数的梯度估计。利用L ∞估计和梯度估计，证明了Dirichlet Laplacian在带边界的紧致流形上的特征函数展开的Hörmander乘子定理.
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.