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Zeitschrift für Analysis und ihre Anwendungen

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Volume 4, Issue 1, 1985, pp. 25–34
DOI: 10.4171/ZAA/134

Published online: 1985-02-28

Embeddings of Sobolev Spaces with Weights of Power Type

David E. Edmunds[1], Alois Kufner[2] and Jiří Rákosník[3]

(1) University of Sussex, Brighton, United Kingdom
(2) University of West Bohemia, Plzen, Czech Republic
(3) Academy of Sciences, Praha, Czech Republic

The paper deals with some properties of the weighted Sobolev spaces $W_0^{k,p}, W_M^{k,p}$ and $H^{k,p}$, with weights which are powers of the distance from a part $M$ of the boundary of the domain of definition. Conditions are given which guarantee the mutual ernbeddings of these spaces and the equivalence of certain norms. The paper generalizes some results of [1] and verifies a conjecture formulated in [2].

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Edmunds David, Kufner Alois, Rákosník Jiří: Embeddings of Sobolev Spaces with Weights of Power Type. Z. Anal. Anwend. 4 (1985), 25-34. doi: 10.4171/ZAA/134