A note on Aubin-Lions-Dubinskii lemmas

Xiuqing Chen Beijing University of Posts and Telecommunications Ansgar Jüngel , Vienna University of Technology Jian-Guo Liu Duke University

Functional Analysis mathscidoc:1702.12001

Acta Appl Math, 133, 33-43, 2014.3
Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinski\u{\i} lemma are proven, refining some recent results in the literature. The first theorem sharpens slightly a result of Dubinski\u{\i} (1965) for seminormed cones. The second theorem applies to piecewise constant functions in time and sharpens slightly the results of Dreher and J\"ungel (2012) and Chen and Liu (2012). An application is given, which is useful in the study of porous-medium or fast-diffusion type equations.
Compactness in Banach spaces· Rothe method · Dubinskii lemma · Seminormed cone
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  title={A note on Aubin-Lions-Dubinskii lemmas},
  author={Xiuqing Chen, Ansgar Jüngel, and Jian-Guo Liu},
  booktitle={Acta Appl Math},
Xiuqing Chen, Ansgar Jüngel, and Jian-Guo Liu. A note on Aubin-Lions-Dubinskii lemmas. 2014. Vol. 133. In Acta Appl Math. pp.33-43. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208001815867015294.
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