Geodesic
Conditions for Embeddings of Sobolev Spaces on a Domain with Anisotropic Peak
Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 51-63

Voir la notice de l'article provenant de la source Math-Net.Ru

For a domain $G\subset \mathbb R^n$ with an anisotropic peak, we construct integral representations of functions in terms of derivatives and establish conditions for the embedding $W_p^s(G)\subset L_q(G)$ of the Sobolev space in the Lebesgue space for $1\leq p$.
Keywords: Sobolev space, domain with a peak, embedding theorem. 
@article{TRSPY_2022_319_a3,
     author = {O. V. Besov},
     title = {Conditions for {Embeddings} of {Sobolev} {Spaces} on a {Domain} with {Anisotropic} {Peak}},
     journal = {Informatics and Automation},
     pages = {51--63},
     publisher = {mathdoc},
     volume = {319},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a3/}
}
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O. V. Besov. Conditions for Embeddings of Sobolev Spaces on a Domain with Anisotropic Peak. Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 51-63. http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a3/