The Dirichlet-to-Neumann operator via hidden compactness
The Dirichlet-to-Neumann operator via hidden compactness
复制标题
通过隐藏紧性的狄利克雷到诺依曼算子
DOI：
10.1016/j.jfa.2013.09.012
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发表时间：
2013
影响因子：
1.7
通讯作者：
Manfred Sauter
中科院分区：
文献类型：
--
作者：
W. Arendt;James B. Kennedy;A. T. Elst;Manfred Sauter
我们证明了对于有界Lipschitz域Ω <$Rd上的每个对称椭圆算子A=−∑ <$k akl <$l+ c，我们可以在L2（<$Ω）上关联一个自伴Dirichlet-to-Neumann算子，如果0在A的Dirichlet谱中，则该算子可以是多值的.为了克服在这种情况下，缺乏连续性，我们采用了一个新版本的Lax-Milgram引理的基础上间接椭圆属性，我们称之为隐藏的紧凑性。然后建立了Dirichlet-to-Neumann算子序列的一致预解式收敛性，只要其系数一致收敛且L2（Ω）中的二阶极限算子具有唯一的连续性.我们还考虑了半群收敛。
We show that to each symmetric elliptic operator of the form A=−∑∂ k a k l∂ l+ c on a bounded Lipschitz domain Ω⊂ R d one can associate a self-adjoint Dirichlet-to-Neumann operator on L 2 (∂ Ω), which may be multi-valued if 0 is in the Dirichlet spectrum of A. To overcome the lack of coerciveness in this case, we employ a new version of the Lax–Milgram lemma based on an indirect ellipticity property that we call hidden compactness. We then establish uniform resolvent convergence of a sequence of Dirichlet-to-Neumann operators whenever the underlying coefficients converge uniformly and the second-order limit operator in L 2 (Ω) has the unique continuation property. We also consider semigroup convergence.