INSTABILITY OF ELLIPTIC EQUATIONS ON COMPACT RIEMANNIAN MANIFOLDS WITH NON-NEGATIVE RICCI CURVATURE

被引：0

作者：

Nascimento, Arnaldo S. ^{[1
]}

Goncalves, Alexandre C. ^{[2
]}

机构：

[1] Univ Fed Sao Carlos, DM, BR-13560 Sao Carlos, SP, Brazil

[2] Univ Sao Paulo, FFCLRP, BR-14049 Ribeirao Preto, SP, Brazil

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年

基金：

巴西圣保罗研究基金会;

关键词：

Riemannian manifold; Ricci curvature; local minimizer; Gamma-convergence; reaction-diffusion equations; REACTION-DIFFUSION EQUATIONS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：18

共 23 条

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