Properties and Uses
- From the continuity of it follows that the function
- is continuous, and its limit as is
- Spherical means are used in finding the solution of the wave equation for with prescribed boundary conditions at
- If is an open set in and is a C2 function defined on, then is harmonic if and only if for all in and all such that the closed ball is contained in one has
- This result can be used to prove the maximum principle for harmonic functions.
Read more about this topic: Spherical Mean
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)