Singularities of harmonic and biharmonic maps into compact manifolds
Singularities of harmonic and biharmonic maps into compact manifolds
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谐波和双调和的奇点映射成紧流形
DOI：
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发表时间：
2017
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通讯作者：
Katarzyna Mazowiecka
中科院分区：
文献类型：
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作者：
Katarzyna Mazowiecka
在满足边界条件u = φ的函数类u：Ω→ R中.后一个事实被称为狄利克雷原理（事实上在1940年被H。Weyl，更多关于拉普拉斯方程的历史观点的细节见[3]）。推广这个概念的一个可能的方法是调和映射的概念。设N是一个光滑的、紧的、没有n维边界的黎曼流形。根据J.Nash的嵌入定理[12]，我们可以假定N等距嵌入到某个欧氏空间R中，且R足够大。对于k ∈ N，1 ≤ p ≤ ∞，我们定义了Sobolev空间
in the class of functions u : Ω→ R satisfying the boundary condition u = φ on ∂Ω. The latter fact is known as the Dirichlet principle (and was in fact proved in 1940 by H. Weyl, for more details on the historical perspective of the Laplace equation see [3]). One of the possible ways to generalize this concept is the notion of harmonic maps. Let N be a smooth, compact Riemannian manifold without boundary of dimension n. According to J. Nash’s embedding theorem [12], we may assume thatN is isometrically embedded in some Euclidean space R for ` su ciently large. For k ∈ N and 1 ≤ p ≤ ∞ we de ne the Sobolev spaces