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On two functionals connected to the Laplacian in a class of doubly connected domains

Published online by Cambridge University Press:  12 July 2007

S. Kesavan
S. Kesavan
Affiliation:
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600 113, India (kesh@imsc.ernet.in)
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Abstract

Let B1 be a ball of radius R1 in RN with centre at the origin and let B0 be a smaller ball of radius R0 contained inside it. Let u be the solution of the problem −Δu = 1 in B1\B0 vanishing on the boundary. It is shown that is minimal if and only if the balls are concentric. It is also shown that the first (Dirichlet) eigenvalue of the Laplacian in B1\B0 is maximal if and only if the balls are concentric. Generalizations are indicated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 3 , June 2003 , pp. 617 - 624
Copyright
Copyright © Royal Society of Edinburgh 2003

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