Closure of Smooth Maps in $W^{1,p}(B^3;S^2)$

Augusto C. Ponce, Jean Van Schaftingen

For every $2<p<3$, we show that $u\in W^{1,p}(B^3;S^2)$ can be strongly approximated by maps in $C^\infty(\Bar{B}^3; S^2)$ if, and only if, the distributional Jacobian of $u$…