SMALL ENERGY COMPACTNESS FOR APPROXIMATE HARMONIC MAPPINGS
SMALL ENERGY COMPACTNESS FOR APPROXIMATE HARMONIC MAPPINGS
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DOI：
10.1142/s0219199711004427
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发表时间：
2011-11
影响因子：
1.6
通讯作者：
Jiayu Li;Xiangrong Zhu
中科院分区：
文献类型：
--
作者：
Jiayu Li;Xiangrong Zhu
本文考虑椭圆型方程组u=-Omega cdot nabla u+f，其中u ∈ W1，2（R2，RK），f ∈ Lln + L，Ω属于反对称的L2（R2，MK（R）<$R2）.在第一部分中，我们证明了该系统的一个紧性定理。作为推论，我们得到了从黎曼曲面到紧致黎曼流形的映射序列的紧性定理，其中张力场在Lln + L中有界。在第二部分中，我们证明了从曲面到球面的映射序列的能量恒等式，其张力场在Lln + L中有界。最后一节我们构造了一个从B_1到S_2的映射序列，其张力场有界于L_ln+ L，但在爆破过程中存在一个正长的颈。
In this paper, we consider the elliptic systems $$ \triangle u=-\Omega \cdot \nabla u+f, $$ where u ∈ W1, 2(R2, RK) and f ∈ L ln+ L, and Ω belongs to L2(R2, MK(R)⊗R2) which is antisymmetric. In the first part we prove a compactness theorem for this system. As a corollary, we obtain the compactness theorem for a sequence of mappings from a Riemannian surface to a compact Riemannian manifold with tension fields bounded in L ln+ L. In the second part we prove the energy identity for a sequence of mappings from a surface to a sphere with tension fields bounded in L ln+ L. In the last section we construct a blow-up sequence of mappings from B1 to S2 with tension fields bounded in L ln+ L but there exists a neck with positive length during blowing up.