Dirihlet problem for the generalized Beltrami equation

Year 2025, Volume: 3 Issue: 1, 12 - 19, 24.06.2025

Pelin Ayşe Gökgöz

Abstract

In this article, we investigate the Dirichlet problem for the generalized Beltrami equation. Firstly, we introduce the solutions of the Dirichlet problem for the inhomogeneous Cauchy-Riemann equation in the unit disc. Secondly, we state the properties of the integral operators for regular domains. Then, by using Banach fixed point theorem, we obtain the existence of the unique solution of the Dirichlet problem for the generalized Beltrami equation in the unit disc.

Keywords

Dirichlet problem, Unit disc, Generalized Beltrami equation, Banach fixed point theorem

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