A Hilbert Boundary Value Problem for Generalised Cauchy-Riemann Equations

被引：0

作者：

Alsaedy, Ammar ^{[1
,2
]}

Tarkhanov, Nikolai ^{[2
]}

机构：

[1] Alnahrain Univ, Dept Math, Coll Sci, Baghdad, Iraq

[2] Univ Potsdam, Inst Math, Karl Liebknecht Str 24-25, D-14476 Golm, Germany

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2017年 / 27卷 / 02期

关键词：

Dirac operator; Clifford algebra; Riemann-Hilbert problem; Fredholm operators;

D O I：

10.1007/s00006-016-0676-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：931 / 953

页数：23

共 50 条

[31] THE GENERALIZED RIEMANN-HILBERT PROBLEM WITH CARLEMAN'S SHIFT AND HIGHER-ORDER DERIVATIVES FOR GENERALIZED CAUCHY-RIEMANN EQUATIONS
何致和
四川师范大学学报(自然科学版), 1991, (01) : 17 - 18
[32] Cauchy-Riemann equations in Minkowski plane
Weiling P.
Advances in Applied Clifford Algebras, 2005, 15 (1) : 71 - 82
[33] Cauchy-riemann equations in convex domains
Polking, John C.
Proceedings of Symposia in Pure Mathematics, 1991,
[34] A Riemann-Hilbert Type Problem for a Singularly Perturbed Cauchy-Riemann Equation with a Singularity in the Coefficient
Fedorov, Yu S.
DIFFERENTIAL EQUATIONS, 2022, 58 (03) : 367 - 380
[35] An Exploring to the Cauchy-Riemann Equations for Proceedings
Zeng, Lijiang
INTERNATIONAL CONFERENCE ON SOCIAL SCIENCE, MANAGEMENT AND ECONOMICS (SSME 2015), 2015, : 750 - 755
[36] SOLUTION OF TANGENTIAL TIAL CAUCHY-RIEMANN EQUATIONS ON Q-CONCAVE CAUCHY-RIEMANN MANIFOLDS
HENKIN, GM
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1981, 292 (01): : 27 - 30
[37] On spectral question of the Cauchy-Riemann operator with homogeneous boundary value conditions
Imanbaev, N. S.
Kanguzhin, B. E.
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2018, 90 (02): : 49 - 55
[38] SOME BOUNDARY VALUE PROBLEMS FOR THE CAUCHY-RIEMANN EQUATION IN HALF LENS
Taghizadeh, N.
Mohammadi, V. Soltani
EURASIAN MATHEMATICAL JOURNAL, 2018, 9 (03): : 73 - 84
[39] Three boundary value problems of the Cauchy-Riemann equation in the Eclipse domain
Emkanpour, Hamed
Taghizadeh, Nasir
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024, 69 (03) : 510 - 529
[40] Two Boundary-Value Problems for the Cauchy-Riemann Equation in a Sector
Wang, Ying
Wang, Yufeng
COMPLEX ANALYSIS AND OPERATOR THEORY, 2012, 6 (06) : 1121 - 1138

← 1 2 3 4 5 →