Rado’s theorem

Theorem (Rado).

Suppose ΩR2 is a convex (http://planetmath.org/ConvexSet) domain (http://planetmath.org/Domain2) with a smooth boundary Ω and suppose that D is the unit disc. Then given any homeomorphismMathworldPlanetmathPlanetmath μ:DΩ, there exists a unique harmonic function u:DΩ such that u=μ on D and u is a diffeomorphismMathworldPlanetmath.


  • 1 R. Schoen, S. T. Yau. . International Press, Inc., Boston, Massachusetts, 1997
Title Rado’s theorem
Canonical name RadosTheorem
Date of creation 2013-03-22 14:08:07
Last modified on 2013-03-22 14:08:07
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 8
Author jirka (4157)
Entry type Theorem
Classification msc 31A05
Related topic HarmonicFunction
Related topic PerronFamily