Nonlinear PDE with vector fields

被引：0

作者：

David Holcman

机构：

[1] Université Pierre et Marie Curie (Paris VI),Mathematical Physics and Geometry of Partial Differential Equations

来源：

Journal d’Analyse Mathématique | 2000年 / 81卷

关键词：

Vector Field; Scalar Curvature; Minimum Point; Sobolev Inequality; Mountain Pass;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A nonlinear PDE on a compact manifold is proposed where we use a given vector field. The nonlinear term involves the critical Sobolev exponent growth. To obtain the existence of solutions, conditions linking a critical point of the field and the scalar curvature are found. The second point is devoted to studying the viscosity limit of the solutions when the Laplacian term tends to zero.

引用

页码：111 / 137

页数：26

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