Sobolev spaces of vector-valued functions

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Caamaño Aldemunde, Iván and Jaramillo Aguado, Jesús Angel and Prieto Yerro, M. Ángeles and Ruiz de Alarcón, Alberto (2020) Sobolev spaces of vector-valued functions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 115 . p. 19. ISSN 1578-7303

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Sobolev spaces; Vector-valued functions
Palabras clave (otros idiomas):Espacios de Sobolev; Funciones vectoriales
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:63349
Deposited On:10 Dec 2020 09:02
Last Modified:10 Dec 2020 11:40

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