Geodesic
On a boundary-value problem for the Poisson equation and the Cauchy--Riemann equation in a lens
Problemy analiza, Tome 14 (2025) no. 1, pp. 77-87

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In this paper, we consider the Dirichlet boundary-value problem for complex partial differential equations in a lens. With the help of the harmonic Green function, the Dirichlet boundary-value problem is solved explicitly for the Poisson equation in a lens. In particular, the boundary behaviors at corner points are considered. In addition, we study the explicit solvability of the Dirichlet boundary-value problem for the homogeneous Cauchy–Riemann equation in the lens.
Keywords: boundary-value problem, Dirichlet problem, Cauchy–Riemann equation
Mots-clés : Poisson equation, lens. 
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     title = {On a boundary-value problem for the {Poisson} equation and the {Cauchy--Riemann} equation in a lens},
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A. Darya; N. Taghizadeh. On a boundary-value problem for the Poisson equation and the Cauchy--Riemann equation in a lens. Problemy analiza, Tome 14 (2025) no. 1, pp. 77-87. http://geodesic.mathdoc.fr/item/PA_2025_14_1_a4/