Yu. G. Reshetnyak, “Sobolev-type classes of functions with values in a metric space. II”, Sibirsk. Mat. Zh., 2004, Volume 45, Number 4,Pages <nobr>855

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Sobolev-type classes of functions with values in a metric space. II

Yu. G. Reshetnyak

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic $n$-dimensional space to a metric space.

Keywords: Sobolev function class, weak derivative, energy functional, function with the Lipschitz condition, separable complete metric space, function with values in metric spaces.

UDC: 517.54

Received: 24.12.2003