A regularity condition in Sobolev spaces \(W_{\operatorname{loc}}^{1,p}(\mathbb{R}^n)\) with \(1\leq p

zbMath1036.26010MaRDI QIDQ1850265

Donatella Bongiorno

Publication date: 1 January 2003

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Lusin's condition (N)differentiability almost everywhereweaker notion of absolute continuity

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Length, area, volume, other geometric measure theory (28A75) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (5)

A local notion of absolute continuity in \(\mathbb R^n\) ⋮ Absolutely continuous functions with values in a Banach space ⋮ Absolute continuity in higher dimensions ⋮ A remark on differentiable functions with partial derivatives in \(L^p\) ⋮ Absolute continuity for Banach space valued mappings

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