Kalidor
Nov30-11, 04:58 AM
I have the statement of a representation formula that goes like this:
"Let O be an open bounded subset of R^n of class C^1. Let u \in C^2(R^n \ cl(O)) be harmonic
and harmonic at infinity. Let u_inf be the limiting value of u at infinity..."
I can't quite follow this, because I thought that under such hypotheses one could already conclude that u must vanish at infinity. I was clearly wrong but then under what additional hypotheses can one say that u vanishes at infinity?
"Let O be an open bounded subset of R^n of class C^1. Let u \in C^2(R^n \ cl(O)) be harmonic
and harmonic at infinity. Let u_inf be the limiting value of u at infinity..."
I can't quite follow this, because I thought that under such hypotheses one could already conclude that u must vanish at infinity. I was clearly wrong but then under what additional hypotheses can one say that u vanishes at infinity?