A Riemann-Hilbert problem for the Moisil-Teodorescu system

  • In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations for a function u with values in R^3 subject to a nonhomogeneous condition (u,v)_x = u_0 on the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem.

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Author:Alexander Polkovnikov, Nikolai Nikolaevich TarkhanovORCiDGND
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (6 (2017) 3)
Document Type:Preprint
Year of Completion:2017
Publishing Institution:Universität Potsdam
Publishing Institution:Universitätsverlag Potsdam
Release Date:2017/06/29
Tag:Dirac operator; Fredholm operators; Riemann-Hilbert problem
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Fxx General first-order equations and systems / 35F45 Boundary value problems for linear first-order systems
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J56 Boundary value problems for first-order elliptic systems
47-XX OPERATOR THEORY / 47Nxx Miscellaneous applications of operator theory [See also 46Nxx] / 47N20 Applications to differential and integral equations
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2017
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht