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Finding values for a harmonic function

StefanM

New member
Jan 30, 2012
28
A function u is harmonic in a domain containing the closed disc x^2+y^2 ≤ 1. Its values on the boundary
are given in terms of the polar angle # by sin# + cos#. Without finding u find
a. its value at the centre of the disc
b. its maximum and minimum values on the closed disc.
The disc is probably defined as D(x,y),r) where r=x^2+y^2 ≤ 1 and I think that the max and minimum can be find on the boundary of the set.But I think that u must also be continuous for that to happen.
Can someone give me a detailed explanation or an example on how to solve this problem?
 

StefanM

New member
Jan 30, 2012
28
What is the best way to solve a and b?
 

Jose27

New member
Feb 1, 2012
15
For a use the mean value property for harmonic functions. For b use the maximum and minimum principle.