This article is cited in 8 papers

Some boundary value problems for the Cauchy–Riemann equation in half lens

N. Taghizadeh, V. Soltani Mohammadi

Faculty of Mathematical Sciences, University of Guilan, Namjoo st, P.O.Box 19141, Rasht, Iran

Abstract: In this article, the boundary behaviour of the Schwarz-type operator on the half lens $\Omega$ 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 $\Omega$ is investigated.

Keywords and phrases: Schwarz-type operator, Schwarz problem, Dirichlet problem, Neumann problem, half lens.

MSC: 30E25, 45E05, 31A10, 35F15

Received: 28.07.2016
Revised: 22.10.2018

Language: English

DOI: 10.32523/2077-9879-2018-9-3-73-84

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