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Titlebook: Complex Methods for Partial Differential Equations; Heinrich G. W. Begehr,A. Okay Celebi,Wolfgang Tuts Book 19991st edition Kluwer Academi

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Hak-Keung Lam,Frank Hung-Fat LeungIn this paper the Neumann problem for the inhomogeneous pluriharmonic system in a polydisc is considered. The definition of the torus (Shilov boundary), the related boundary function for a polydisc, the solvability conditions and the explicit solution which is unique up to an arbitrary additive constant are given.
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System with Imprecise Jumping Parameters,Second order Cauchy Pompeiu formulas are given in the case of one and of several complex variables, for Douglis-algebra-valued functions of one complex variable and for Clifford-algebra-valued functions of several real variables. The kernels of the integral operators attained provide fundamental solutions for the respective differential operators.
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Stability Analysis of Neural NetworksA classical result in complex analysis which is an important point in the study of the Hilbert transform (and therefore of singular integral transforms) on ℝ, and which is quite relevant to boundary value problems of different kinds is the following:
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https://doi.org/10.1007/978-3-319-27200-9The Dirichlet problem is considered for a nonlinear Beltrami equation and for a quasilinear biharmonic equation. Reducing the problems via integral equations to fixed point problems the solutions are considered in different function spaces and then compared with one another.
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On some Problems for First Order Elliptic Systems in the Plane,In this paper, we study solvability problems for elliptic system of equations of first order with singular coefficients, as well as nonlinear boundary value problems. Some models are investigated.
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