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Reflections on Dubinskiĭ's nonlinear compact embedding theorem
2012
Publications de l'Institut Mathématique (Beograd)
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We present an overview of a result by Ju. A. Dubinskii [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; A_0), where A_0 is a Banach space and p ∈ [1,∞]; we establish a variant of Dubinskii'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 E. Maitre [Int. J. Math. Math. Sci. 27 (2003)].
doi:10.2298/pim1205095b
fatcat:qta5n76ys5hv5mwzlxbstwuzvy