Instability results for an elliptic equation on compact Riemannian manifolds with non-negative Ricci curvature

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We prove nonexistence of nonconstant local minimizers for a class of functionals, which typically appears in the scalar two-phase field model, over a smooth N-dimensional Riemannian manifold without boundary with non-negative Ricci curvature. Conversely for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative we prove existence of nonconstant local minimizers for the same class of functionals.
26 pages

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Differential Geometry, Functional Analysis, 35J20; 58J05

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http://salesiana.dossiersoluciones.com/handle/123456789/163883

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0806.4885
 http://arxiv.org/abs/0806.4885

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arXiv