Global Minimality and Rigidity of the Constraint Map Vortex

Bin Deng, Jiahuan Li, Yilu Liu +1

We consider the minimization problem \[ \min\left\{\int_{B_1}|Du|^2:\ u\in W^{1,2}(B_1;\mathbb R^n),\quad u=x\ \text{on }\partial B_1,\quad |u|\ge a\right\}, \quad 0<a<1. \] Figall…