学术报告十二：Boundary bubbling analysis of approximate harmonic maps under weak anchoring condition in

(高水平大学建设系列报告082)

We consider a sequence of weakly convergent,  approximate harmonic maps $u_k$ from a two dimensional domain $\Omega$ into a compact Rimenanian manifold $(N,h)$ under a weak anchoring condition $g:\partial\Omega\to N$, which can be viewed as critical points of $$1/2\int_\Omega (|Du|^2+\langle\tau, u\rangle)+w/2\int_{\partial\Omega}|u-g|^2,$$ where $\tau$ is a given tension field.  Under mild conditions on $\tau_k$ and $g_k$, we obtain a global energy quantization result, which account for the loss of energy by a finite number of harmonic $2$ spheres. This is a joint work with Tao Huang, NYU-Shanghai.

Changyou Wang received his PhD at Rice University at 1996, and is currently a Professor of Mathematics at Purdue University. His research interests are nonlinear partial differential equations arising from geometric variational problems, calculus of variations, and applied mathematics.

2017-06-05