2026-06-27T22:59:42Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/75992024-07-12T15:09:02Zcom_20.500.14352_14col_20.500.14352_15

Sobolev spaces of vector-valued functions Caamaño Aldemunde, Iván Jaramillo Aguado, Jesús Ángel Prieto Yerro, M. Ángeles Ruiz de Alarcón, Alberto 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. 2023-06-17T08:56:22Z 2023-06-17T08:56:22Z 2023-06-17T08:56:22Z 2020-11-09 journal article https://hdl.handle.net/20.500.14352/7599 1578-7303 10.1007/s13398-020-00959-4 eng PGC2018-097286-B-I00 open access Springer