Variational properties of a nonlinear elliptic equation and rigidity

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dc.creatorBialy, M. L.
dc.creatorMacKay, R. S.
dc.date1999-02-02
dc.date.accessioned2026-07-07T05:27:45Z
dc.date.available2026-07-07T05:27:45Z
dc.descriptionWe consider in this paper elliptic equations which are perturbations of Laplace's equation by a compactly supported potential. We show that in dimension greater than three for a wide class of potentials all the solutions are globally minimising. However, in dimension two the situation is different. We show that for radially symmetric potentials there always exist solutions which are not locally minimal unless the potential vanishes identically. We discuss the relations of this with the so-called Hopf rigidity phenomenon.
dc.description11 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/9902016
dc.identifierhttp://arxiv.org/abs/math/9902016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78042
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.titleVariational properties of a nonlinear elliptic equation and rigidity
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