harmonic function
A twice-differentiable real or complex-valued function or , where is some , is called harmonic if its Laplacian vanishes on , i.e. if
Any harmonic function or satisfies Liouville’s theorem. Indeed, a holomorphic function is harmonic, and a real harmonic function , where , is locally the real part of a holomorphic function. In fact, it is enough that a harmonic function be below (or above) to conclude that it is .
Title | harmonic function |
Canonical name | HarmonicFunction |
Date of creation | 2013-03-22 12:43:46 |
Last modified on | 2013-03-22 12:43:46 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 9 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 31C05 |
Classification | msc 31B05 |
Classification | msc 31A05 |
Classification | msc 30F15 |
Related topic | RadosTheorem |
Related topic | SubharmonicAndSuperharmonicFunctions |
Related topic | DirichletProblem |
Related topic | NeumannProblem |