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A Hilbert boundary value problem for generalised Cauchy-Riemann equations

  • We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.

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Author:Ammar Alsaedy, Nikolai Nikolaevich TarkhanovORCiDGND
ISSN:2193-6943 (online)
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (5 (2016) 1)
Publisher:Universitätsverlag Potsdam
Place of publication:Potsdam
Document Type:Preprint
Year of first Publication:2016
Year of Completion:2016
Publishing Institution:Universität Potsdam
Publishing Institution:Universitätsverlag Potsdam
Release Date:2016/01/12
Tag:Clifford algebra; Dirac operator; Fredholm operator; 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
Publication Way:Universitätsverlag Potsdam
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2016
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht