Spectral problems in Sobolev-type Banach spaces for strongly elliptic systems in Lipschitz domains

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• 作者：M. S. Agranovich
• 刊名：Mathematische Nachrichten
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：289
• 期：16
• 页码：1968-1985
• 全文大小：253K
• ISSN：1522-2616

文摘

This paper is devoted to classical spectral boundary value problems for strongly elliptic second-order systems in bounded Lipschitz domains, in general non-self-adjoint, namely, to questions of regularity and completeness of root functions (generalized eigenfunctions), resolvent estimates, and summability of Fourier series with respect to the root functions by the Abel–Lidskii method in Sobolev-type spaces. These questions are not difficult in the Hilbert spaces of the type spaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">H1=H21, and important results in this case are well-known, but our aim is to extend the results to Banach spaces spaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">Hps with spaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">(s,p) in a neighborhood of (1, 2). We also touch upon some spectral problems on Lipschitz boundaries. Tools from interpolation theory of operators are used, especially the Shneiberg theorem.