649- Homework Assignment #4                               

                                    (Due by 2/15/06)

 

    Let  be Green’s function for Laplace’s equation on a simply

connected domain , with a smooth boundary , where  is a corrector function.

By definition  for every and .

 is therefore harmonic in  and  continuous on .  Prove that  

by applying the maximum/minimum principle for Laplace’s equation to, and then to.

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                                        C.O. Bloom