FRIEDLANDER'S EIGENVALUE INEQUALITIES AND THE DIRICHLET-TO-NEUMANN SEMIGROUP
FRIEDLANDER'S EIGENVALUE INEQUALITIES AND THE DIRICHLET-TO-NEUMANN SEMIGROUP
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DOI：
10.3934/cpaa.2012.11.2201
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发表时间：
2012-11-01
影响因子：
1
通讯作者：
Mazzeo, Rafe
中科院分区：
文献类型：
--
作者：
Arendt, Wolfgang;Mazzeo, Rafe
如果Omega是任意紧的Lipschitz域，可能在黎曼流形中，且边界Gamma=偏导数Omega，则对于任何实Lambda，Dirichlet-to-Neumann算子D-lambda被定义在L-2(Gamma)上。我们证明了D-lambda的特征值与Robin Laplace Delta(Mu)的特征值之间的密切关系，即带有Robin边界条件的偏导数(Nu)u=Mu.这是Neumann和Dirichlet特征值Lambda(N)(k+1)之间Friedlander不等式的又一证明.
If Omega is any compact Lipschitz domain, possibly in a Riemannian manifold, with boundary Gamma = partial derivative Omega, the Dirichlet-to-Neumann operator D-lambda is defined on L-2(Gamma) for any real lambda. We prove a close relationship between the eigenvalues of D-lambda and those of the Robin Laplacian Delta(mu), i.e. the Laplacian with Robin boundary conditions partial derivative(nu)u = mu u. This is used to give another proof of the Friedlander inequalities between Neumann and Dirichlet eigenvalues, lambda(N)(k+1)