The Stokes Dirichlet-to-Neumann operator

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-03-15 DOI:10.1007/s00028-023-00930-x

C. Denis, A. F. M. ter Elst

引用次数: 0

Abstract

Let \(\Omega \subset \mathbb {R}^d\) be a bounded open connected set with Lipschitz boundary. Let \(A^N\) and \(A^D\) be the Stokes Neumann operator and Stokes Dirichlet operator on \(\Omega \), respectively. We study the associated Stokes version of the Dirichlet-to-Neumann operator and show a Krein formula which relates these three Stokes version operators. We also prove a Stokes version of the Friedlander inequalities, which relates the Dirichlet eigenvalues and the Neumann eigenvalues.

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斯托克斯迪里赫勒到诺伊曼算子

让（\Omega \subset \mathbb {R}^d\）是一个有界的开阔连通集合，具有 Lipschitz 边界。让 \(A^N\) 和 \(A^D\) 分别是 \(\Omega \) 上的斯托克斯诺伊曼算子和斯托克斯狄利克特算子。我们研究了相关的斯托克斯版本的狄利克特到诺伊曼算子，并展示了一个将这三个斯托克斯版本算子联系起来的克林公式。我们还证明了弗里德兰德不等式的斯托克斯版本，它将狄利克特特征值和诺伊曼特征值联系起来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators