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.