Geodesic
Embedding of Sobolev Spaces and Properties of the Domain
Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 343-349

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We establish the embedding of the Sobolev space $W_p^s(G)\subset L_q(G)$ 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 $G$.
Keywords: Sobolev space, Sobolev embedding theorem, domain with flexible $\sigma$-cone condition, Hölder's inequality, Marcinkiewicz interpolation theorem. 
@article{MZM_2014_96_3_a3,
     author = {O. V. Besov},
     title = {Embedding of {Sobolev} {Spaces} and {Properties} of the {Domain}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {343--349},
     publisher = {mathdoc},
     volume = {96},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a3/}
}
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O. V. Besov. Embedding of Sobolev Spaces and Properties of the Domain. Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 343-349. http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a3/