Conformal mappings that satisfy the boundary condition of equality of metrics (Q1377943)
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scientific article; zbMATH DE number 1113089
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Conformal mappings that satisfy the boundary condition of equality of metrics |
scientific article; zbMATH DE number 1113089 |
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Conformal mappings that satisfy the boundary condition of equality of metrics (English)
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14 July 1998
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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.
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conformal mapping
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boundary condition
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