On the Dirichlet Boundary Value Problem for the Cauchy-Riemann Equations in the Half Disc
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Ada Academica
2024-05-01
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| Series: | European Journal of Mathematical Analysis |
| Online Access: | https://adac.ee/index.php/ma/article/view/227 |
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| Summary: | 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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| ISSN: | 2733-3957 |