Area, coarea, and approximation in W1,1

David Swanson

doi:10.1007/s11512-007-0051-z

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Home > Journals > Ark. Mat. > Volume 45 > Issue 2 > Article

October 2007 Area, coarea, and approximation in W^1,1

David Swanson

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David Swanson¹
¹Department of Mathematics, University of Louisville

Ark. Mat. 45(2): 381-399 (October 2007). DOI: 10.1007/s11512-007-0051-z

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Abstract

Let Ω⊂ℝⁿ be an arbitrary open set. We characterize the space W^1,1_loc(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 W^1,1(ℝⁿ).