Kesavan, S. (2003) On two functionals connected to the Laplacian in a class of doubly connected domains Proceedings of the Royal Society of Edinburgh: A - Mathematics, 133 . pp. 617-624. ISSN 0308-2105
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Official URL: http://journals.cambridge.org/action/displayAbstra...
Related URL: http://dx.doi.org/10.1017/S0308210500002560
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 ∫B1\B0|Δu|2dx 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Royal Society of Edinburgh. |
| ID Code: | 16347 |
| Deposited On: | 15 Nov 2010 13:49 |
| Last Modified: | 03 Jun 2011 11:47 |
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