On Boundary Value Problems for an Improperly Elliptic Equation in a Circle

Burskii, V. P.; Lesina, E. V.

doi:10.1134/s0965542520080059

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2024

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Cited by 2 publications

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“…Many results have been obtained for boundary value problems of complex partial differential equations in some particular domains, see, e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In the year 2009, Harmonic boundary value problem for the Poisson equation in a half disc was presented by H. Begehr and T. Vaitekhovich [2].…”

Section: Pmentioning

confidence: 99%

On the Dirichlet Boundary Value Problem for the Cauchy-Riemann Equations in the Half Disc

Darya,

Tagizadeh

2024

Eur. J. Math. Anal.

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In this article, we investigate the Dirichlet boundary value problem for the Cauchy-Riemann equations in the half disc. First, using the technique of parqueting–reflection and the Cauchy-Pompeiu representation formula for a half disc, we obtain an integral representation formula in the half disc. In other words, we construct a unique solution for the Dirichlet boundary value problem. Finally, we solve the Dirichlet boundary value problem for both the homogeneous and the inhomogeneous Cauchy-Riemann equations. In particular, the boundary behaviors at the corner points are considered.

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