Abstract:
We establish the embedding of the Sobolev space Wsp(G)⊂Lq(G) for an irregular domain G in the case of a limit exponent under new relations between the parameters depending on the geometric properties of the domain G.
Citation:
O. V. Besov, “Embedding of Sobolev Spaces and Properties of the Domain”, Mat. Zametki, 96:3 (2014), 343–349; Math. Notes, 96:3 (2014), 326–331
This publication is cited in the following 17 articles:
O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on a Hölder Domain in Lebesgue Spaces”, Math. Notes, 113:1 (2023), 18–26
O. V. Besov, “Integral Representations and Embeddings of Spaces of Functions of Positive Smoothness on a Hölder Domain”, Proc. Steklov Inst. Math., 323 (2023), 47–58
Jiri Vala, Vladislav Kozak, Petra Jarosova, “On a Computational Approach to Micro- and Macro-modelling of Damage in Brittle and Quasi-brittle Materials”, International Journal of Mechanics, 14 (2020), 185
O. V. Besov, “Embeddings of spaces of functions of positive smoothness on irregular domains”, Dokl. Math., 99:1 (2019), 31–35
O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains”, Math. Notes, 106:4 (2019), 501–513
O. V. Besov, “Embeddings for weighted spaces of functions of positive smoothness on irregular domains into Lebesgue spaces”, Dokl. Math., 97:3 (2018), 236–239
O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Spaces”, Math. Notes, 103:3 (2018), 348–356
O. V. Besov, “Embeddings of Weighted Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Space”, Math. Notes, 104:6 (2018), 799–809
O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Math. Notes, 101:4 (2017), 608–618
E. I. Berezhnoi, V. V. Kocherova, A. A. Perfilyev, “Notes for Trudinger-Moser inequality”, International Conference Functional Analysis In Interdisciplinary Applications (FAIA 2017), AIP Conference Proceedings, 1880, eds. T. Kalmenov, M. Sadybekov, Amer Inst Physics, 2017, UNSP 030009
O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Proc. Steklov Inst. Math., 293 (2016), 56–66
D. V. Prokhorov, “On a Set Everywhere Dense in a Lebesgue Space on the Real Line”, Math. Notes, 100:4 (2016), 639–641
O. V. Besov, “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687
O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Dokl. Math., 93:1 (2016), 13–15
O. V. Besov, “Embedding of a weighted Sobolev space and properties of the domain”, Proc. Steklov Inst. Math., 289 (2015), 96–103
V. D. Stepanov, “On Optimal Banach Spaces Containing a Weight Cone of Monotone or Quasiconcave Functions”, Math. Notes, 98:6 (2015), 957–970
O. V. Besov, “Embedding of a weighted Sobolev space and properties of the domain”, Dokl. Math., 90:3 (2014), 754–757
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