maximum principle
- Maximum principle
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Let (where ) be a harmonic function. Then attains its extremal values on any compact on the boundary of . If attains an extremal value anywhere in the interior of , then it is constant.
- Maximal modulus principle
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Let (where ) be a holomorphic function. Then attains its maximal value on any compact on the boundary of . If attains its maximal value anywhere on the interior of , 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 |