RT Journal Article
T1 Sobolev spaces of vector-valued functions
A1 Caamaño Aldemunde, Iván
A1 Jaramillo Aguado, Jesús Ángel
A1 Prieto Yerro, M. Ángeles
A1 Ruiz de Alarcón, Alberto
AB We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset Ω ⊂ R N and a Banach space V , we compare the classical Sobolev space W1,p(Ω, V ) with the so-called Sobolev-Reshetnyak space R1,p(Ω, V ). We see that, in general, W1,p(Ω, V ) is a closed subspace of R1,p(Ω, V ). As a main result, we obtain that W1,p(Ω, V ) = R1,p(Ω, V ) if, and only if, the Banach space V has the Radon-Nikod´ym property.
PB Springer
SN 1578-7303
YR 2020
FD 2020-11-09
LK https://hdl.handle.net/20.500.14352/7599
UL https://hdl.handle.net/20.500.14352/7599
LA eng
NO Ministerio de Ciencia, Innovación y Universidades (España)
DS Docta Complutense
RD 6 abr 2025