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Funktsional'nyi Analiz i ego Prilozheniya, 2011, Volume 45, Issue 1, Pages 1–15
DOI: https://doi.org/10.4213/faa3031 (Mi faa3031) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface

M. S. Agranovich

Moscow Institute of Electronics and Mathematics
Full-text PDF (267 kB) Citations (11)
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DOI: https://doi.org/10.4213/faa3031
Abstract: 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 $H^s$, the simplest $L_2$-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.
Keywords: strong ellipticity, Lipschitz domain, nonclosed boundary, potential type operators, Bessel potential spaces, Besov spaces, regularity of solutions, spectral transmission problems, spectral asymptotics.
Received: 28.04.2010
English version:
Functional Analysis and Its Applications, 2011, Volume 45, Issue 1, Pages 1–12
DOI: https://doi.org/10.1007/s10688-011-0001-1
Bibliographic databases:
Document Type: Article
UDC: 517.98+517.95
Language: Russian
Citation: M. S. Agranovich, “Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 1–15; Funct. Anal. Appl., 45:1 (2011), 1–12
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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