Finding values for a harmonic function

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SUMMARY

The harmonic function u defined in the closed disc x^2+y^2 ≤ 1 has its boundary values expressed as sin(#) + cos(#). The value at the center of the disc can be determined using the mean value property for harmonic functions, which states that the value at the center is the average of the boundary values. The maximum and minimum values of u on the closed disc can be found using the maximum and minimum principle, which asserts that these extrema occur on the boundary of the domain.

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Stephen88
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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?
 
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What is the best way to solve a and b?
 
For a use the mean value property for harmonic functions. For b use the maximum and minimum principle.
 

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