科研之友
微信
新浪微博
Facebook
分享链接
摘要
We are interested in some energy functionals concentrated on the discontinuity lines of divergence-free 2D vector fields valued in the circle S-1. This kind of energy has been introduced first by Aviles and Giga (A mathematical problem related to the physical theory of liquid crystal configurations, 1987). They show in particular that, with the cubic cost function f (t) = t(3), this energy is lower semicontinuous. In this paper, we construct a counter-example which excludes the lower semicontinuity of line energies for cost functions of the form t(p) with 0 < p < 1. We also show that, in this case, the viscosity solution corresponding to a certain convex domain is not a minimizer.
- 出版日期2017-2
