On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms |
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Authors: | M H C Anisa A R Aithal |
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Institution: | (1) Department of Mathematics, University of Mumbai, 400 098 Mumbai, India |
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Abstract: | LetB
1
be a ball of radiusr
1
inS
n
(ℍn), and letB
0
be a smaller ball of radiusr
0
such thatB
0
⊂B
1
. ForS
n
we considerr
1
π. Let u be a solution of the problem- δm = 1 in Ω :=B
1
/B
0
vanishing on the boundary. It is shown that the associated functionalJ (Ω) is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian
on Ω is maximal if and only if the balls are concentric. |
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Keywords: | Eigenvalue problem Laplacian maximum principles |
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