Conformal mappings that satisfy the boundary condition of equality of metrics
type: Item
instance of: scholarly article
title: Conformal mappings that satisfy the boundary condition of equality of metrics
zbMATH Open document ID: 0890.30025
published in: Doklady Mathematics
publication date: 1998-07-14T00:00:00Z
review text: The author considers the problem of reconstructing a conformal mapping \(f: D\to G\) by the boundary condition \[ {|dw|\over \varphi (w)}= {|dz |\over \psi (z)},\;w= f(z),\;z\in \partial D, \] where \(D\) and \(G\) are plane domains, \(0\in D\), \(f(0) =0\), \(f'(0)>0\); \(\varphi, \psi\) are given functions. The existence of a solution and its properties in two classes of functions are studied. The proofs are sketched.
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 30C35
Mathematics Subject Classification ID: 31A25
Mathematics Subject Classification ID: 35J55
zbMATH DE Number: 1113089
zbMATH Keywords: conformal mapping
zbMATH Keywords: boundary condition
author: F. G. Avkhadiev
reviewed by: Zbigniew Binderman
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1113089