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

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

2009-01-28

arxiv.org/abs/0901.4491v1

Differential Integral Equations 22 (2009), no. 9-10, 881-900

Mathematics

Functional Analysis

16 pages

Scientific paper

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 $u$ vanishes identically. This result was originally
proved by Bethuel-Coron-Demengel-Helein, but we present a different strategy
which is motivated by the $W^{2,p}$-case.

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