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On a comparison theorem via symmetrisation

Published online by Cambridge University Press:  14 November 2011

S. Kesavan
S. Kesavan
Affiliation:
Tata Institute of Fundamental Research, Bangalore Centre, IISc Campus, P.O. Box 1234, Bangalore 560 012, India
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Synopsis

Talenti's theorem allows us to estimate the norms of the solution of an elliptic boundary value problem posed on a bounded open set Ω in terms of those of the “symmetrised” problem posed on Ω*, the ball centred at 0 and such that |Ω| = |Ω*|. We are interested in the limiting case when equality is achieved between the norms of the two solutions. We show then that Ω = Ω* and that the solution is radially symmetric and decreasing. The novelty of this exposition is that the method used is very elementary compared to the usual arguments.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 119 , Issue 1-2 , 1991 , pp. 159 - 167
Copyright
Copyright © Royal Society of Edinburgh 1991

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