maximum principle


Maximum principle

Let f:U (where Ud) be a harmonic functionPlanetmathPlanetmath. Then f attains its extremal values on any compact KU on the boundary K of K. If f attains an extremal value anywhere in the interior of K, then it is constant.

Maximal modulus principle

Let f:U (where U) be a holomorphic functionMathworldPlanetmath. Then |f| attains its maximal value on any compact KU on the boundary K of K. If |f| attains its maximal value anywhere on the interior of K, then it is constant.

Title maximum principle
Canonical name MaximumPrinciple
Date of creation 2013-03-22 12:46:06
Last modified on 2013-03-22 12:46:06
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Theorem
Classification msc 30C80
Classification msc 31A05
Classification msc 31B05
Classification msc 30F15
Synonym maximal modulus principle
Synonym maximum principle for harmonic functions
Related topic HadamardThreeCircleTheorem
Related topic PhragmenLindelofTheorem