Open Access
September/October 2009 Closure of smooth maps in $W^{1,p}(B^3;S^2)$
Augusto C. Ponce, Jean Van Schaftingen
Differential Integral Equations 22(9/10): 881-900 (September/October 2009). DOI: 10.57262/die/1356019513


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.


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Augusto C. Ponce. Jean Van Schaftingen. "Closure of smooth maps in $W^{1,p}(B^3;S^2)$." Differential Integral Equations 22 (9/10) 881 - 900, September/October 2009.


Published: September/October 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.46063
MathSciNet: MR2553061
Digital Object Identifier: 10.57262/die/1356019513

Primary: 58D15
Secondary: 46E35 , 46T20

Rights: Copyright © 2009 Khayyam Publishing, Inc.

Vol.22 • No. 9/10 • September/October 2009
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