2. Let 2 be an open set in R" with n ≥ 3, and u be a harmonic function in N. Let & € R¹ and A> 0. Define Prove that αξ,λ u૬,A(T) := := 1 |x - ε|n-20 u (ε + № ²(x=0)). - 5/1²). is harmonic in its domain.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. Let 2 be an open set in R" with n ≥ 3, and u be a harmonic function in N. Let & € Rn and
> > 0. Define
1²(x-E)
X
|x - §|n-2
u‹,x(x):
Prove that αξ,λ is harmonic in its domain.
=
-U
ε +
Transcribed Image Text:2. Let 2 be an open set in R" with n ≥ 3, and u be a harmonic function in N. Let & € Rn and > > 0. Define 1²(x-E) X |x - §|n-2 u‹,x(x): Prove that αξ,λ is harmonic in its domain. = -U ε +
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