One-dimensional half-harmonic maps into the circle and their degree

Luca Martinazzi, Ali Hyder

Given a half-harmonic map $u\in {\dot{H}}^{\frac{1}{2},2}(\mathbb{R},{\mathbb{S}}^1)$ minimizing the fractional Dirichlet energy under Dirichlet boundary conditions in $\mathbb{R}\setmi…