Solution of harmonic problems with mixed boundary conditions for lunate domains (Q2753473)
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scientific article; zbMATH DE number 1670293
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solution of harmonic problems with mixed boundary conditions for lunate domains |
scientific article; zbMATH DE number 1670293 |
Statements
11 November 2001
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bipolar coordinates
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lunate domain
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Laplace equation
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Carleman problem
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singular integral equation
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infinite algebraical system
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0.8918771
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0.8899287
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0.8841619
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0.8783685
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0.87623334
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0.8760884
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Solution of harmonic problems with mixed boundary conditions for lunate domains (English)
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Laplace equation for a lunate domain in bipolar coordinates is solved. At one of the boundaries, the condition of the first or the second kind is prescribed while at the other boundary the condition of the third kind is prescribed. The lunate domain is conformally mapped onto an infinite strip and a functional equation with respect to the unknown function is derived. Then the obtained Carleman problem is reduced to a singular integral equation of the second kind with the Cauchy kernel. The latter equation is reduced to an infinite system of algebraical equations. In a special case an exact solution of the problem is found.
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