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A remark on comparison results via symmetrization

Published online by Cambridge University Press:  14 November 2011

A. Alvino ,
P.L. Lions  and
G. Trombetti
A. Alvino
Affiliation:
Istituto di Matematica, Universita di Napoli, Via Mezzocannone, 8, 80134 Naples, Italy
P.L. Lions
Affiliation:
CEREMADE, Université Paris IX-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France
G. Trombetti
Affiliation:
Istituto di Matematica, Universita di Napoli, Via Mezzocannone, 8, 80134 Naples, Italy
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Synopsis

In this paper, we study the converse of comparison results for solutions to linear second-order elliptic equations. Namely, in the inequalities proved by G. Talenti and others, we study the case of equality and prove that “equalities are achieved only in the spherical situation”. We also present some applications of these results to semilinear elliptic equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 1-2 , 1986 , pp. 37 - 48
Copyright
Copyright © Royal Society of Edinburgh 1986

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