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.
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
Section: Chapter Questions
Problem 1RQ
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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 +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49a3f886-5843-4971-a881-41b2ba018dcc%2F2b27ed05-2f6d-4d7e-8ded-4d81c9de8c2c%2Fjo8bc0a_processed.jpeg&w=3840&q=75)
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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