Reflections on Dubinskii's nonlinear compact embedding theorem

Journal article

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 $L^p(0,T; \mathcal{A}_0)$, where $\mathcal{A}_0$ is a Banach space and $p \in [1,\infty]$; 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)].

Authors: Barrett, J; Süli, E

• Publication status: Published
• Journal: Publ. Inst. Math. (Belgrade) (N.S.) 91(105) (2012), 95-110
• Volume: 91
• Issue: 105
• Pages: 95-110
• Publication date: 2011-01-10
• DOI: 10.2298/PIM1205095B
• EISSN: 1820-7405
• ISSN: 0350-1302
• Language: English
• Keywords: math.AP; math.FA