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arXiv · 0901.4491

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

Augusto C. Ponce·Jean Van Schaftingen
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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 $C^\infty(\Bar{B}^3; S^2)$ 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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Augusto C. Ponce, Jean Van Schaftingen. 2009-01-28. Closure of Smooth Maps in $W^{1,p}(B^3;S^2)$. https://arxiv.org/abs/0901.4491

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