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Integral representations in the complex plane and iterated boundary value problems
Rocky Mountain Journal of Mathematics, 2022In the attempt to develop a theory for complex partial differential equations, the study of model equations are a first necessity. In recent years polyanalytic and polyharmonic differential operators were studied in relation to boundary value problems. They are mainly the Schwarz boundary value problem for the polyanalytic and Dirichlet, Neumann, Robin
Akel, Mohamed +2 more
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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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Boundary-Value Problems for the Helmholtz Equation in Domains of the Complex Plane
Ukrainian Mathematical Journal, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Local uniqueness of a boundary value problem in the complex plane
Asymptotic Analysis, 1993We will consider the following boundary value problem for a second-order linear differential equation with polynomial coefficients in the complex plane: is there a differential equation of the specific type with linearly independent solutions y 1 (x) and y 2
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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 ...
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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 ...
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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 ...
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Integral Equations and Operator Theory, 2010
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Applied Mathematics and Mechanics, 2017
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Journal of Soviet Mathematics, 1993
The paper presents a brief survey of the available methods of automatic triangulation of two-dimensional regions. A technique proposed for nonhomogeneous regions of complex structure ensures compact representation of the input data and generates nearly uniform triangular meshes. This technique is applied to an example.
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The paper presents a brief survey of the available methods of automatic triangulation of two-dimensional regions. A technique proposed for nonhomogeneous regions of complex structure ensures compact representation of the input data and generates nearly uniform triangular meshes. This technique is applied to an example.
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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,
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