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- May 19th 2010, 02:40 PM #1
## PDE problem

Let be a bounded set with smooth boundary. Assume that and are and that they satisfy:

in

on

and

in

on

where and are continuous functions.

Assume that for on . Prove that

for

State any theorems used in the proof.

Since I know that for .

I need to justify that where .

Since the laplacian is negative I know that and .

This is where I get my problem. , and do not necessarily imply that for .

Can anyone help?