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On some boundary value problems on a strip in the complex plane
Reports on Mathematical Physics, 2003The Sommerfeld integral inversion method for the Helmholtz equation in an angular region with different boundary values leads to boundary value problems in an infinite strip of the complex plane. The author investigates a generic system for such boundary value problems and gives the existence and uniqueness results with optimal growth estimates on the ...
W. Durand
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Journal of Mathematical Sciences, 2017
In the paper the conformal mappings of simply connected domains onto the circle are used to construct bases in the spaces of functions being analytical in these domains. The obtained basic functions are bi-orthogonal with the Faber polynomials. Based on the analytical functions expansions into series in basic functions systems, the solutions of ...
M. Sukhorolsky
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In the paper the conformal mappings of simply connected domains onto the circle are used to construct bases in the spaces of functions being analytical in these domains. The obtained basic functions are bi-orthogonal with the Faber polynomials. Based on the analytical functions expansions into series in basic functions systems, the solutions of ...
M. Sukhorolsky
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Ukrainian Mathematical Journal, 1996 See the review in Zbl 0887.35031.
Бурский, В.П.
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Complex Variables, Theory and Application: An International Journal, 1994
In Refs. [1], [2] and [4], we discussed the discontinuous Riemann-hilbert boundary value problems for nonlinear uniformly elliptic complex equations of first order in a multiply connected plane domain, but, there the solution for the modified boundary value problem with the indeces ...
Guo-Chun Wen, Chung-Chun Yang
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In Refs. [1], [2] and [4], we discussed the discontinuous Riemann-hilbert boundary value problems for nonlinear uniformly elliptic complex equations of first order in a multiply connected plane domain, but, there the solution for the modified boundary value problem with the indeces ...
Guo-Chun Wen, Chung-Chun Yang
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Basic complex boundary value problems in in the upper half plane
2006In der Analysis spielen Integraldarstellungen für Funktionen eine bedeutende Rolle. Dies gilt insbesondere im Hinblick auf gewöhnliche und partielle Differentialgleichungen. Solche Differentialgleichungen wiederum tauchen bei den meisten Problemen der angewandten Mathematik auf. In der Regel werden Integraldarstellungen auf reguläre Gebiete formuliert,
E. Gaertner
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Integral Equations and Operator Theory, 2010
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V. Ryzhov
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V. Ryzhov
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COMPLEX BOUNDARY VALUE PROBLEMS IN A QUARTER PLANE
Complex Analysis and Applications, 2006H. BEGEHR, G. HARUTYUNYAN
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Complex boundary value problems on a circular triangle
Complex Variables and Elliptic Equations, 2023We apply the parqueting-reflection technique for a triangle domain to achieve the points of the complex plane. Then the Cauchy–Schwarz representation formula is construed by the Cauchy–Pompeiu formula and an explicit solution for the Schwarz boundary ...
Hamed Emkanpour, N. Taghizadeh
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Three boundary value problems of the Cauchy–Riemann equation in the Eclipse domain
Complex Variables and Elliptic Equations, 2022In this article, by the parqueting-reflection technique, we obtain a covering of the complex plane from reflecting the Eclipse domain. Then, by the Cauchy–Pompeiu formula, we derive the generalized Cauchy–Pompeiu representation formula in the Eclipse ...
Hamed Emkanpour, N. Taghizadeh
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On divergence type linear and quasilinear equations in the complex plane
Ukrainian Mathematical Bulletin, 2023This is a survay of our recent results concerning divergence type linear and quasilinear equations in the complex plane. It contains a number of existence, representation and regularity theorems for solutions of fundamental boundary value problems for ...
V. Gutlyanskiǐ +3 more
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