Reflections on Dubinskiĭ’s nonlinear compact embedding theorem

Abstract

We present an overview of a result by Yuliĭ Andreevich Dubinskiĭ [Mat. Sb. 67 (109) (1965); translated in Amer. Math. Soc. Transl. (2) 67 (1968)], concerning the compact embedding of a seminormed set in Lp(0, T;A0), where A0 is a Banach space and p 2 [1,1]; 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 Emmanuel Maitre [Int. J. Math. Math. Sci. 27 (2003)].