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October 2007 Area, coarea, and approximation in W1,1
David Swanson
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Ark. Mat. 45(2): 381-399 (October 2007). DOI: 10.1007/s11512-007-0051-z


Let Ω⊂ℝn be an arbitrary open set. We characterize the space W1,1loc(Ω) using variants of the classical area and coarea formulas. We use these characterizations to obtain a norm approximation and trace theorems for functions in the space W1,1(ℝn).


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David Swanson. "Area, coarea, and approximation in W1,1." Ark. Mat. 45 (2) 381 - 399, October 2007.


Received: 27 December 2005; Published: October 2007
First available in Project Euclid: 31 January 2017

zbMATH: 1163.46302
MathSciNet: MR2342611
Digital Object Identifier: 10.1007/s11512-007-0051-z

Rights: 2007 © Institut Mittag-Leffler

Vol.45 • No. 2 • October 2007
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