Geodesic
Reflections on Dubinskiĭ's Nonlinear Compact Embedding Theorem
Publications de l'Institut Mathématique, _N_S_91 (2012) no. 105, p. 95

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We present an overview of a result by Yuli{\u\i} Andreevich Dubinski{\u\i} [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{\u\i}'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 : 46B50 46E40 35K99 
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     author = {John W. Barrett and Endre S\"uli},
     title = {Reflections on {Dubinski\u{i}'s} {Nonlinear} {Compact} {Embedding} {Theorem}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {95 },
     publisher = {mathdoc},
     volume = {_N_S_91},
     number = {105},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2012_N_S_91_105_a8/}
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John W. Barrett; Endre Süli. Reflections on Dubinskiĭ's Nonlinear Compact Embedding Theorem. Publications de l'Institut Mathématique, _N_S_91 (2012) no. 105, p. 95 . http://geodesic.mathdoc.fr/item/PIM_2012_N_S_91_105_a8/