Reflections on Dubinskiǐ's nonlinear compact embedding theorem

Abstract

We present an overview of a result by Yuliǐ Andreevich Dubinskiǐ [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 Dubinskiǐ'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.