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Hopf fibration and singularly perturbed elliptic equations

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


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