Energy concentration for almost harmonic maps and the Willmore functional
Energy concentration for almost harmonic maps and the Willmore functional
复制标题
近调和映射和威尔莫尔泛函的能量集中
DOI：
10.1007/s00209-005-0803-z
复制
发表时间：
2005
影响因子：
0.8
通讯作者：
R. Moser
中科院分区：
文献类型：
--
作者：
R. Moser
设Ω是Ω_3或Ω_4中的开域，N是光滑的紧致黎曼流形。我们考虑映射u：Ω→N的Dirichlet能量E（u）及其负L2梯度，张力场τ（u）.我们研究了映射ui：Ω→N的序列，
如果映射是充分正则的，我们发现了远离Ω中广义子流形的强H1-次收敛。如果极限映射也是正则的，我们可以估计这个广义子流形的Willmore型能量。
AbstractLet Ω be an open domain in ℝ3 or ℝ4 and N a smooth, compact Riemannian manifold. We consider the Dirichlet energy E(u) for maps u:Ω→N and its negative L2-gradient, the tension field τ(u). We study sequences of maps ui:Ω→N with
If the maps are sufficiently regular, we find strong H1-subconvergence away from a generalized submanifold in Ω. If the limit map is regular, too, we can estimate a Willmore-type energy of this generalized submanifold.