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:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)