Hopf fibration and  singularly perturbed elliptic equations

Bernhard Ruf; P. N. Srikanth

doi:10.3934/dcdss.2014.7.823

Article Contents

2014, Volume 7, Issue 4: 823-838. Doi: 10.3934/dcdss.2014.7.823

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Hopf fibration and singularly perturbed elliptic equations

Bernhard Ruf^1, and
P. N. Srikanth^2,

1.
Dip. di Matematica, Universita degli Studi, Via Saldini 50, 20133 Milano
2.
T.I.F.R. CAM, Bangalore, 560065

Received: October 31, 2013

Revised: November 30, 2013

Published: July 2014

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Abstract

In this article we show how the Hopf fibration can be used to generate special solutions of singularly perturbed elliptic equations on annuli. Indeed, by the Hopf fibration the equation can be reduced to a lower dimensional problem, to which known results on single (or multiple point) concentration can be applied. Reversing the reduction process, one obtains solutions concentrating on circles and spheres, which are given as the fibres of the Hopf fibration.

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Mathematics Subject Classification: Primary: 35J61, 35J20; Secondary: 35B25.

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