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单词 MaximumPrinciple
释义

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.

Titlemaximum principle
Canonical nameMaximumPrinciple
Date of creation2013-03-22 12:46:06
Last modified on2013-03-22 12:46:06
Ownermathcam (2727)
Last modified bymathcam (2727)
Numerical id5
Authormathcam (2727)
Entry typeTheorem
Classificationmsc 30C80
Classificationmsc 31A05
Classificationmsc 31B05
Classificationmsc 30F15
Synonymmaximal modulus principle
Synonymmaximum principle for harmonic functions
Related topicHadamardThreeCircleTheorem
Related topicPhragmenLindelofTheorem
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