Publications de l'Institut Mathématique, Nouvelle SérieVol. 91(105), pp. 95–110 (2012)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 91(105), pp. 95–110 (2012) |
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REFLECTIONS ON DUBINSKII'S NONLINEAR COMPACT EMBEDDING THEOREMJohn W. Barrett and Endre SüliDepartment of Mathematics, Imperial College London, London SW7 2AZ, UK and Mathematical Institute, University of Oxford, Oxford OX1 3LB, UKAbstract: 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 Full text of the article: (for faster download, first choose a mirror)
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
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