XI: 03, 27-33, LNM 581 (1977)
CHUNG, Kai Lai
Pedagogic notes on the barrier theorem (
Potential theory)
Let $D$ a bounded open set in $
R^n$, and let $z$ be a boundary point. Then a barrier at $z$ is a superharmonic function in $D$, strictly positive and with a limit equal to $0$ at $z$. The barrier theorem asserts that if there is a barrier at $z$, then $z$ is regular. An elegant proof of this is given using Brownian motion. Then it is shown that the expectation of $S$, the hitting time of $D^c$, is bounded, upper semi-continuous in $R^n$ and continuous in $D$, and is a barrier at every regular point
Comment: An error is corrected in
1247Keywords: Classical potential theory,
Barrier,
Regular pointsNature: New proof of known results
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