We consider weakly convergent sequences of approximate H-surface maps defined in the plane with their tension fields bounded in 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 . 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.
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| Shenzhou Zheng |
Department of Mathematics, Beijing Jiaotong University
Beijing 100044, China
email: firstname.lastname@example.org, Phone: +86-10-51688449
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