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Harmonic function 
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#1
Dec405, 09:45 AM

P: 276

I am to find a function U, harmonic on the disk [tex] x^2 + y^2 < 6 [/tex] and satisfying
[tex] u(x, y) = y + y^2 [/tex] on the disk's boundary. I am not sure where to start. Hints, help, anything? 


#2
Dec405, 09:49 AM

Sci Advisor
HW Helper
P: 9,398

Use the integral formula.



#3
Dec405, 09:53 AM

PF Gold
P: 864

I would think Cauchy's integral formual would be useful here: you have the value of a function on a boudry and want the value in the interior.



#4
Dec405, 07:00 PM

P: 76

Harmonic function
You are trying to solve the Laplace equation on a disk. Try seperation of variables, then break it down to 2 ODE's. Here is a start for you..
You will probably need to solve the PDE in polar coordinates.  harsh 


#5
Dec405, 11:01 PM

P: 276




#6
Dec405, 11:08 PM

P: 76

 harsh 


#7
Dec505, 06:59 AM

P: 276




#8
Dec505, 09:21 AM

P: 76

The theta condition that you are going to use, I believe, will be that theta is 2pi periodic.
 harsh 


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