REFLECTIONS ON DUBINSKIĬ’S NONLINEAR COMPACT EMBEDDING THEOREM
John W. Barrett, Endre S Üli · 2011
Abstract. We present an overview of a result by Ju. A. Dubinskiĭ [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; A0), where A0 is a Banach space and p ∈ [1, ∞]; we establish a variant of Dubinskiĭ’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)]. 1.