Harmonic Dirichlet problem in a ring sector. (English) Zbl 1323.31004
Mityushev, Vladimir V. (ed.) et al., Current trends in analysis and its applications. Proceedings of the 9th ISAAC congress, Kraków, Poland, August 5–9, 2013. Cham: Birkhäuser/Springer (ISBN 978-3-319-12576-3/pbk; 978-3-319-12577-0/ebook). Trends in Mathematics. Research Perspectives, 67-75 (2015).
Summary: In this paper, we construct a harmonic Green function by reflection method in a general ring sector with angle \(\theta=\frac{\pi}{\alpha}\) and \(\alpha\geq\frac{1}{2}\), then the related harmonic Dirichlet problem for the Poisson equation is discussed explicitly.
For the entire collection see [Zbl 1308.00055].
For the entire collection see [Zbl 1308.00055].
MSC:
| 31A05 | Harmonic, subharmonic, superharmonic functions in two dimensions |
| 31A30 | Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions |
| 30E25 | Boundary value problems in the complex plane |
| 31A25 | Boundary value and inverse problems for harmonic functions in two dimensions |
References:
| [1] | Begehr, H.; Gaertner, E. A., A Dirichlet problem for the inhomogeneous polyharmonic equation in the upper half plane, Georgian Math. J., 14, 1, 33-52 (2007) · Zbl 1141.31001 |
| [2] | Begehr, H.; Vaitekhovich, T., Harmonic boundary value problems in half disc and half ring, Funct. Approx., 40, 2, 251-282 (2009) · Zbl 1183.30039 · doi:10.7169/facm/1246454030 |
| [3] | Shupeyeva, B., Harmonic boundary value problems in a quarter ring domain, Adv. Pure Appl. Math., 3, 393-419 (2012) · Zbl 1281.31003 |
| [4] | Begehr, H.; Vaitekhovich, T., Iterated Dirichlet problem for the higher order Poisson equation, Matematiche, LXIII, 139-154 (2008) · Zbl 1193.31002 |
| [5] | Wang, Y.; Wang, Y., Schwarz-type problem of nonhomogeneous Cauchy-Riemann equation on a triangle, J. Math. Anal. Appl., 377, 2, 557-570 (2011) · Zbl 1208.30039 · doi:10.1016/j.jmaa.2010.11.023 |
| [6] | Begehr, H., Complex Analytic Methods for Partial Differential Equations: an Introductory Text (1994), Singapore: World Scientific, Singapore · Zbl 0840.35001 · doi:10.1142/2162 |
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