## Differential and Integral Equations

### Closure of smooth maps in $W^{1,p}(B^3;S^2)$

#### Abstract

For every $2 < p < 3$, we show that $u \in W^{1,p}(B^3;S^2)$ can be strongly approximated by maps in $C^\infty(\overline B \,\!^3;S^2)$ if, and only if, the distributional Jacobian of $u$ vanishes identically. This result was originally proved by Bethuel-Coron-Demengel-H\'elein, but we present a different strategy which is motivated by the $W^{2,p}$-case.

#### Article information

Source
Differential Integral Equations, Volume 22, Number 9/10 (2009), 881-900.

Dates
First available in Project Euclid: 20 December 2012

Ponce, Augusto C.; Van Schaftingen, Jean. Closure of smooth maps in $W^{1,p}(B^3;S^2)$. Differential Integral Equations 22 (2009), no. 9/10, 881--900. https://projecteuclid.org/euclid.die/1356019513