Abstract
We consider a class of completely regular polyhedrons \(\mathfrak {N} \) and prove direct and inverse embedding theorems for different dimensions (i.e., theorems on the traces) for functions in the Sobolev multianisotropic space \( W^{\mathfrak {N}}_2(\mathbb {R}^3)\).
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REFERENCES
G. V. Demidenko, Sobolev Spaces and Generalized Solutions (Novosib. State Univ., Novosibirsk, 2015) [in Russian].
H. G. Ghazaryan, “The Newton polyhedron, spaces of differentiable functions and general theory of differential equations,” Arm. J. Math. 9, 102 (2017).
G. A. Karapetyan, “Integral representations of functions and embedding theorems for multianisotropic spaces on the plane with one anisotropy vertex,” Izv. Nats. Akad. Nauk Arm. Mat. 51, no. 6, 23 (2016) [J. Contemp. Math. Anal., Arm. Acad. Sci. 51:6, 269 (2016)].
G. A. Karapetyan, “Integral representation and embedding theorems for \(n \)dimensional multianisotropic spaces with one anisotropic vertex,” Sib. Mat. Zh. 58, 573 (2017) [Sib. Math. J. 58, 445 (2017)].
G. A. Karapetyan, “An integral representation and embedding theorems in the plane for multianisotropic spaces,” Izv. Nats. Akad. Nauk Arm. Mat. 52, no. 6, 12 (2017) [J. Contemp. Math. Anal. Arm. Acad. Sci. 52:6, 267 (2017)].
G. A. Karapetyan and M. K. Arakelyan, “Estimation of multianisotropic kernels and their application to the embedding theorems,” Trans. Razmadze Math. Inst. 171, 48 (2017).
G. A. Karapetyan and M. K. Arakelyan, “Embedding theorems for general multianisotropic spaces,” Mat. Zam. 104, 422 (2018) [Math. Notes 104, 417 (2018)].
G. A. Karapetyan and H. A. Petrosyan, “Embedding theorems for multianisotropic spaces with two vertices of anisotropicity,” Proc. Yerevan State Univ. Phys. Math. Sci. 51, 29 (2017).
M. A. Khachaturyan and A. R. Akopyan, “On the traces of functions in multianisotropic Sobolev spaces,” Vestn. Ross.-Arm. Univ. Fiz.-Mat. Estestv. Nauki, no. 1, 55 (2021) [in Russian].
L. N. Slobodetskiĭ, “Generalized Sobolev spaces and their application to boundary problems for partial differential equations,” Uch. Zap. Leningr. Gos. Ped. Inst. 197, 54 (1958) [Am. Math. Soc. Transl. II. Ser. 57, 207 (1966)].
S. L. Sobolev, Some Applications of Functional Analysis to Mathematical Physics (Nauka, Moscow, 1988; Am. Math. Soc., Providence, R.I., 1991).
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Khachaturyan, M.A. Direct and Inverse Embedding Theorems for Different Dimensions for a Class of Multianisotropic Sobolev Spaces. Sib. Adv. Math. 34, 91–97 (2024). https://doi.org/10.1134/S1055134424020019
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DOI: https://doi.org/10.1134/S1055134424020019