On two functionals connected to the Laplacian in a class of doubly connected domains
2003 ◽
Vol 133
(3)
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pp. 617-624
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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.
2015 ◽
Vol 66
(5)
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pp. 2419-2440
2007 ◽
Vol 280
(12)
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pp. 1354-1362
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2015 ◽
Vol 160
(2)
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pp. 191-208
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1995 ◽
Vol 101
(3)
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pp. 363-369
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2012 ◽
Vol 23
(3)
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pp. 1427-1440
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