Boundary bubbling analysis of approximate harmonic maps under either   weak or strong anchoring conditions in dimension two
  In this paper, we will study the bubbling phenomena of approximate harmonic maps in dimension two that have either (i) bounded $L^2$-tension fields under the weak anchoring condition, or (ii) bounded $L\log L \cap M^{1,\delta}$-tension fields under the strong anchoring condition. 
Tao Huang and Changyou Wang
math.AP