# Poincaré problem

From Encyclopedia of Mathematics

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=15422

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article