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Difference between revisions of "Poincaré problem"

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To find a [[Harmonic function|harmonic function]] in a bounded simply-connected domain <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p073/p073080/p0730801.png" /> which, on the boundary <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p073/p073080/p0730802.png" /> of the domain, satisfies the condition
 
To find a [[Harmonic function|harmonic function]] in a bounded simply-connected domain <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p073/p073080/p0730801.png" /> which, on the boundary <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p073/p073080/p0730802.png" /> of the domain, satisfies the condition
  

Revision as of 15:04, 2 May 2012


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To find a harmonic function in a bounded simply-connected domain which, on the boundary of the domain, satisfies the condition

where , , , and are real-valued functions given on , is the arc parameter and is the normal to . H. Poincaré (1910) arrived at this problem while working on the mathematical theory of fluid flow and gave an (incomplete) solution to the problem in case , and the contour and the functions and are analytic.

See also Boundary value problems of analytic function theory.

How to Cite This Entry:
Poincaré problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Poincar%C3%A9_problem&oldid=23486
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article