Spectral stability for a class of fourth order Steklov problems under domain perturbations
Spectral stability for a class of fourth order Steklov problems under domain perturbations
复制标题
DOI：
10.1007/s00526-018-1481-0
复制
发表时间：
2019-02-01
影响因子：
2.1
通讯作者：
Lamberti, Pier Domenico
中科院分区：
文献类型：
--
作者：
Ferrero, Alberto;Lamberti, Pier Domenico
研究了两个四阶Steklov问题在区域扰动下的谱稳定性。其中一个问题是经典的DBSDirichlet双调和Steklov问题，另一个问题是它的一个变种.在较弱的区域收敛条件下，我们证明了两个问题的预解算子的稳定性，这意味着特征值和特征函数的稳定性。本征函数的稳定性估计用强H2-范数表示。进行分析，而不假设域是星形的。至少对于DBS问题的变体，我们的条件是尖锐的。在DBS问题的情况下，我们证明了一个合适的Dirichlet到Neumann型映射的稳定性在非常弱的条件下的收敛域，我们制定了一个公开的问题。作为我们的分析的旁路产品，我们提供了一些稳定性和不稳定性的Navier和Navier型边值问题的双调和算子。
We study the spectral stability of two fourth order Steklov problems upon domain perturbation. One of the two problems is the classical DBSDirichlet Biharmonic Steklovproblem, the other one is a variant. Under a comparatively weak condition on the convergence of the domains, we prove the stability of the resolvent operators for both problems, which implies the stability of eigenvalues and eigenfunctions. The stability estimates for the eigenfunctions are expressed in terms of the strong H2-norms. The analysis is carried out without assuming that the domains are star-shaped. Our condition turns out to be sharp at least for the variant of the DBS problem. In the case of the DBS problem, we prove stability of a suitable Dirichlet-to-Neumann type map under very weak conditions on the convergence of the domains and we formulate an open problem. As bypass product of our analysis, we provide some stability and instability results for Navier and Navier-type boundary value problems for the biharmonic operator.