Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 177, pp. 1-13.

Title: Energy quantization for approximate H-surfaces and applications 

Author: Shenzhou Zheng (Beijing Jiaotong Univ., Beijing, China)

Abstract:
 We consider weakly convergent sequences of approximate H-surface maps
 defined in the plane with their tension fields bounded in $L^p$ for
 p> 4/3, and establish an energy quantization that accounts for
 the loss of their energies by the sum of energies over finitely many
 nontrivial bubbles maps on $\mathbb{R}^2$. As a direct consequence,
 we establish the energy identity at finite singular time to their
 H-surface flows.

Submitted February 2, 2013. Published July 30, 2013.
Math Subject Classifications: 35J50, 35K40, 58D15.
Key Words: Approximate H-surface maps; energy quantization;
           H-surface flows; concentration of energy; bubbling phenomena.