EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 91(105), pp. 95–110 (2012)

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John W. Barrett and Endre Süli

Department of Mathematics, Imperial College London, London SW7 2AZ, UK and Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK

Abstract: We present an overview of a result by Yuli{\ui} Andreevich Dubinski{\ui} [Mat. Sb. 67 (109) (1965); translated in Amer. Math. Soc. Transl. (2) 67 (1968)], concerning the compact embedding of a seminormed set in $L^p(0,T;\cA_0)$, where $\mathcal{A}_0$ is a Banach space and $p\in[1,\infty]$; we establish a variant of Dubinski{\ui}'s theorem, where a seminormed nonnegative cone is used instead of a seminormed set; and we explore the connections of these results with a nonlinear compact embedding theorem due to Emmanuel Maitre [Int. J. Math. Math. Sci. 27 (2003)].

Classification (MSC2000): 46B50, 46E40; 35K99

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Electronic fulltext finalized on: 10 May 2012. This page was last modified: 12 Jun 2012.

© 2012 Mathematical Institute of the Serbian Academy of Science and Arts
© 2012 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition