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- Title
SMALL ENERGY COMPACTNESS FOR APPROXIMATE HARMONIC MAPPINGS.
- Authors
LI, JIAYU; ZHU, XIANGRONG
- Abstract
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.
- Publication
Communications in Contemporary Mathematics, 2011, Vol 13, Issue 5, p741
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199711004427