Exercise 42 (LIOUVILLE theorem)
Exercises
Index
© 2002-2007 Prof. Dr. Hans Wilhelm Alt, University of Bonn, Germany
Exercise 43 (GREEN function for halve space)
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GREEN function for halve space
[aufgabe:43]
Sei
Ω:={x∈
R
n
; x
n
>0} und u∈C
2
(
clos
(Ω)) harmonisch. Ferner gelte für ein β>0
lim sup
|x| → ∞
|x|
β
|u(x)|<∞.
Leite folgende POISSON-Darstellung für x∈Ω her:
u(x)=
2
ϭ
n
∫
R
n-1
x
n
|x-(ỹ,0)|
n
u(ỹ,0) dỹ.
Version 1.5
H.W. Alt - 02.01.2007
Exercise 42 (LIOUVILLE theorem)
Exercises
Index
© 2002-2007 Prof. Dr. Hans Wilhelm Alt, University of Bonn, Germany
