Strongly elliptic second-order systems with boundary conditions on a nonclosed Lipschitz surface
Strongly elliptic second-order systems with boundary conditions on a nonclosed Lipschitz surface
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非封闭 Lipschitz 曲面上具有边界条件的强椭圆二阶系统
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发表时间：
2011
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通讯作者：
M. Agranovich
中科院分区：
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作者：
M. Agranovich
研究具有Lipschitz边界的紧致非闭Lipschitz曲面S上具有边界条件的强椭圆型二阶系统的边值问题和传输问题。本文的主要目的是利用S上的势型算子，在最简单的Sobolev型l2 -空间Hs中找到这些问题的唯一可解性的条件。我们还首先讨论了更一般的Bessel势空间和Besov空间中解的正则性，其次讨论了S上传输条件下带谱参数问题的谱性质，包括特征值的渐近性。
We consider boundary value problems and transmission problems for strongly elliptic second-order systems with boundary conditions on a compact nonclosed Lipschitz surface S with Lipschitz boundary. The main goal is to find conditions for the unique solvability of these problems in the spaces Hs, the simplest L2-spaces of the Sobolev type, with the use of potential type operators on S. We also discuss, first, the regularity of solutions in somewhat more general Bessel potential spaces and Besov spaces and, second, the spectral properties of problems with spectral parameter in the transmission conditions on S, including the asymptotics of the eigenvalues.