On symmetry results for elliptic   equations with convex nonlinearities

Kanishka Perera; Marco Squassina

doi:10.3934/cpaa.2013.12.3013

Article Contents

2013, Volume 12, Issue 6: 3013-3026. Doi: 10.3934/cpaa.2013.12.3013

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On symmetry results for elliptic equations with convex nonlinearities

Kanishka Perera^1, and
Marco Squassina^2,

1.
Department of Mathematical Sciences, Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901
2.
Dipartimento di Informatica, Università degli Studi di Verona, Cá Vignal 2, Strada Le Grazie 15, I-37134 Veron

Received: September 30, 2012

Revised: February 28, 2013

Published: October 2013

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Abstract

We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric. The semi-linear problems are studied in a framework where the associated functional is of class $C^1$ but not of class $C^2$.

Keywords:

Semi-linear and quasi-linear elliptic equation,
full and partial symmetry.

Mathematics Subject Classification: 35D99, 35J62, 58E05, 35J70.

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References

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