Exterior Neumann problem

I have no idea what you mean by this. The "exterior VonNeumann problem" for a closed curve is to be given a partial differential equation and want to find the function which satisfies the differential equation outside the curve while having a specified value on the curve. But what does it mean for a problem to "hold"?

At first I thought you meant "cannot be solved" but that is trivially not true. The problem with the differential equation \(\displaystyle \nabla^2\phi= 0\), and \(\displaystyle \phi(x,y)= 1\) on the unit circle has the solution \(\displaystyle \phi(x,y)= 1\) for all x, y.
 
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HallsofIvy said:
I have no idea what you mean by this. The "exterior VonNeumann problem" for a closed curve is to be given a partial differential equation and want to find the function which satisfies the differential equation outside the curve while having a specified value on the curve. But what does it mean for a problem to "hold"?

At first I thought you meant "cannot be solved" but that is trivially not true. The problem with the differential equation \(\displaystyle \nabla^2\phi= 0\), and \(\displaystyle \phi(x,y)= 1\) on the unit circle has the solution \(\displaystyle \phi(x,y)= 1\) for all x, y.
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Dear HallsofIvy
I have proof of Interior Neumann Problem for a circle but my sir told me that Exterior Nuemann Problem for circle does not exists?so my quaestion is, why exterios neumann problem for circle does not exists?
 
What do you mean by "does not exist"? A problem, in general, may be solvable or not but I don't see a sense in which the problem itself "does not exist".
 
Where did you get the idea that it isn't solvable? Exactly what "exterior Neumann problem" are you talking about?
 
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