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Proceedings of the Royal Society of Edinburgh Section A: Mathematics Proceedings of the Royal Society of Edinburgh Section A: Mathematics

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Symmetry of solutions to optimization problems related to partial differential equations

Published online by Cambridge University Press:  12 July 2007

Fabrizio Cuccu  and
Giovanni Porru
Fabrizio Cuccu
Affiliation:
Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italyfcuccu@unica.it
Giovanni Porru
Affiliation:
Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italyporru@unica.it
Corresponding
E-mail address:
fcuccu@unica.it
porru@unica.it
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Abstract

We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving-plane method to find symmetry results for solutions of a system. We apply these results in our discussion of symmetry for the maximal configurations of the previous problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 5 , October 2006 , pp. 921 - 934
Copyright
Copyright © Royal Society of Edinburgh 2006

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