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Funktsional'nyi Analiz i ego Prilozheniya, 2009, Volume 43, Issue 3, Pages 3–25
DOI: https://doi.org/10.4213/faa2964
(Mi faa2964)
 

This article is cited in 19 scientific papers (total in 19 papers)

Potential Type Operators and Transmission Problems for Strongly Elliptic Second-Order Systems in Lipschitz Domains

M. S. Agranovich

Moscow State Institute of Electronics and Mathematics
References:
Abstract: We consider a strongly elliptic second-order system in a bounded $n$-dimensional domain $\Omega^+$ with Lipschitz boundary $\Gamma$, $n\ge2$. The smoothness assumptions on the coefficients are minimized. For convenience, we assume that the domain is contained in the standard torus $\mathbb{T}^n$. In previous papers, we obtained results on the unique solvability of the Dirichlet and Neumann problems in the spaces $H^\sigma_p$ and $B^\sigma_p$ without use of surface potentials. In the present paper, using the approach proposed by Costabel and McLean, we define surface potentials and discuss their properties assuming that the Dirichlet and Neumann problems in $\Omega^+$ and the complementing domain $\Omega^-$ are uniquely solvable. In particular, we prove the invertibility of the integral single layer operator and the hypersingular operator in Besov spaces on $\Gamma$. We describe some of their spectral properties as well as those of the corresponding transmission problems.
Keywords: strongly elliptic system, Lipschitz domain, Dirichlet problem, Neumann problem, Bessel potential space, Besov space, surface potential, transmission problem.
Received: 19.01.2009
English version:
Functional Analysis and Its Applications, 2009, Volume 43, Issue 3, Pages 165–183
DOI: https://doi.org/10.1007/s10688-009-0025-y
Bibliographic databases:
Document Type: Article
UDC: 517.98+517.95
Language: Russian
Citation: M. S. Agranovich, “Potential Type Operators and Transmission Problems for Strongly Elliptic Second-Order Systems in Lipschitz Domains”, Funktsional. Anal. i Prilozhen., 43:3 (2009), 3–25; Funct. Anal. Appl., 43:3 (2009), 165–183
Citation in format AMSBIB
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\paper Potential Type Operators and Transmission Problems for Strongly Elliptic Second-Order Systems in Lipschitz Domains
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  • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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