Abstract:
In this article, the boundary behaviour of the Schwarz-type operator on the half lens Ω will be discussed and the existence of boundary values at corner points is proved. Finally, two basic boundary value problems, namely, Dirichlet and Neumann problems for analytic functions and more generally the Dirichlet problem for the inhomogeneous Cauchy–Riemann equation in Ω is investigated.
Citation:
N. Taghizadeh, V. Soltani Mohammadi, “Some boundary value problems for the Cauchy–Riemann equation in half lens”, Eurasian Math. J., 9:3 (2018), 73–84
\Bibitem{TagSol18}
\by N.~Taghizadeh, V.~Soltani Mohammadi
\paper Some boundary value problems for the Cauchy--Riemann equation in half lens
\jour Eurasian Math. J.
\yr 2018
\vol 9
\issue 3
\pages 73--84
\mathnet{http://mi.mathnet.ru/emj306}
\crossref{https://doi.org/10.32523/2077-9879-2018-9-3-73-84}
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https://www.mathnet.ru/eng/emj306
https://www.mathnet.ru/eng/emj/v9/i3/p73
This publication is cited in the following 8 articles:
A. Darya, N. Taghizadeh, “On a boundary-value problem for the Poisson equation and the Cauchy–Riemann equation in a lens”, Probl. anal. Issues Anal., 14:1 (2025), 77–87
A. Darya, N. Taghizadeh, “Schwarz Boundary Value Problem for the Polyanalytic Equation in a Lens”, Sib Math J, 66:2 (2025), 486
Hamed Emkanpour, Nasir Taghizadeh, “Three boundary value problems of the Cauchy–Riemann equation in the Eclipse domain”, Complex Variables and Elliptic Equations, 69:3 (2024), 510
A. Darya, N. Taghizadeh, “Three Boundary Value Problems for Complex Partial Differential Equations in the Lens Domain”, Comput. Math. and Math. Phys., 64:6 (2024), 1295
Ali Darya, Nasir Taghizadeh, “SCHWARZ AND DIRICHLET PROBLEMS FOR COMPLEX PARTIAL DIFFERENTIAL EQUATIONS IN THE PARTIAL ECLIPSE DOMAIN”, J Math Sci, 2024
Heinrich Begehr, “Hyperbolic tessellation: harmonic Green function for a Schweikart triangle in hyperbolic geometry*”, Complex Variables and Elliptic Equations, 2024, 1
A. Darya, N. Tagkhizadekh, “Zadachi Shvartsa i Dirikhle dlya ¯∂-uravneniya v treugolnoi oblasti”, Izv. vuzov. Matem., 2024, no. 11, 12–22
A. Darya, N. Taghizadeh, “Schwarz and Dirichlet Problems for ¯∂-Equation in a Triangular Domain”, Russ Math., 68:11 (2024), 9
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