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Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary
-
Yiqian Shi
and
Bin Xu
Published/Copyright:
March 1, 2013
Abstract.
Let 
be an eigenfunction
with respect to the Dirichlet Laplacian 
on a compact
Riemannian manifold N with boundary: 
in the interior of N and 
on the boundary of N. We
show the following gradient estimate on 
: for every 
, there holds 
, where C is a positive
constant depending only on N. In the proof, we use a basic
geometrical property of nodal sets of eigenfunctions and elliptic
a priori estimates.
Keywords: Dirichlet eigenfunction; gradient estimate
Received: 2010-05-18
Revised: 2010-11-17
Published Online: 2013-03-01
Published in Print: 2013-03-01
© 2013 by Walter de Gruyter Berlin Boston
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- Non-Lipschitz flow of the nonlinear Schrödinger equation on surfaces
- Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary
- A composite map in the stable homotopy groups of spheres
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