Spectral problems in Lipschitz domains
Spectral problems in Lipschitz domains
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Lipschitz 域中的谱问题
DOI：
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发表时间：
2013
期刊：
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通讯作者：
M. Agranovich
中科院分区：
文献类型：
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作者：
M. Agranovich
本文研究有界Lipschitz域上二阶强椭圆系统的谱问题。我们考虑了谱Dirichlet问题和Neumann问题以及三个带谱参数的边值问题：Poincaré-Steklov问题和两个透射问题。在风格的调查，我们讨论了这些问题的主要性质，包括自伴和非自伴。作为一个初步的，我们解释了几个事实的一般理论的主要边值问题的Lipschitz域。最初的定义是可变的。边界势的使用是基于Dirichlet和Neumann问题的唯一可解性的结果。在本文的主要部分，我们使用最简单的Hilbert L~2-空间Hs，但我们描述了一些推广到Banach空间Hsp的Bessel潜力和Besov空间Bsp在文章的最后。
The paper is devoted to spectral problems for strongly elliptic second-order systems in bounded Lipschitz domains. We consider the spectral Dirichlet and Neumann problems and three problems with spectral parameter in conditions at the boundary: the Poincaré–Steklov problem and two transmission problems. In the style of a survey, we discuss the main properties of these problems, both self-adjoint and non-self-adjoint. As a preliminary, we explain several facts of the general theory of the main boundary value problems in Lipschitz domains. The original definitions are variational. The use of the boundary potentials is based on results on the unique solvability of the Dirichlet and Neumann problems. In the main part of the paper, we use the simplest Hilbert L2-spaces Hs, but we describe some generalizations to Banach spaces Hsp of Bessel potentials and Besov spaces Bsp at the end of the paper.