Arnaldo S. Nascimento, Alexandre C. Gonçalves
Abstract:
We prove the nonexistence of nonconstant local minimizers for a
class of functionals, which typically appear in scalar
two-phase field models,
over smooth N-dimensional Riemannian manifolds
without boundary and non-negative Ricci curvature.
Conversely, for a class of surfaces possessing a simple closed
geodesic along which the Gauss curvature is negative, we prove
the existence of nonconstant local minimizers for the same class
of functionals.
Submitted November 15, 2009. Published May 8, 2010.
Math Subject Classifications: 35J20, 58J05.
Key Words: Riemannian manifold; Ricci curvature; local minimizer;
Gamma-convergence; reaction-diffusion equations.
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| Arnaldo S. Nascimento Universidade Federal de São Carlos DM, São Carlos, SP, Brazil email: arnaldon@dm.ufscar.br |
| Alexandre C. Gonçalves Universidade de São Paulo FFCLRP, Ribeirão Preto, SP, Brazil email: acasa@ffclrp.usp.br |
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