Necessary and sufficient conditions for the chain rule in \(W_{\text{loc}}^{1,1} (\mathbb R^N;\mathbb R^d)\) and \(BV_{\text{loc}}(\mathbb R^N;\mathbb R^d)\)

DOI10.4171/JEMS/78zbMath1135.26011OpenAlexW2016832830MaRDI QIDQ997826

Massimiliano Morini, Giovanni Leoni

Publication date: 7 August 2007

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=9&iss=2&rank=2

zbMATH Keywords

Sobolev spacefunction of bounded variationchain ruledifferentiability of Lipschitz functions

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) Continuity and differentiation questions (26B05) Calculus of vector functions (26B12) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Representation and superposition of functions (26B40)

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