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Strict convexity of level sets of solutions of some nonlinear elliptic equations

Published online by Cambridge University Press:  12 July 2007

Francesca Gladiali  and
Massimo Grossi
Francesca Gladiali
Affiliation:
Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P. le A. Moro 2, 00185 Roma, Italy (gladiali@mat.uniroma1.it)
Massimo Grossi
Affiliation:
Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P. le A. Moro 2, 00185 Roma, Italy (grossi@mat.uniroma1.it)
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Abstract

In this paper we study the convexity of the level sets of solutions of the problem where f is a suitable function with subcritical or critical growth. Under some assumptions on the Gauss curvature of ∂Ω, we prove that the level sets of the solution of (0.1) are strictly convex.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 2 , April 2004 , pp. 363 - 373
Copyright
Copyright © Royal Society of Edinburgh 2004

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