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
Biography
Changyou Wang is Professor at Purdue University. His main research interests are the nonlinear partial differential equations, calculus of variations, geometrical analysis and application of geometry measure theory, especially harmonic maps and heat flow equations, biharmonic maps and heat flow equations, liquid crystal flows.