This article is cited in 9 papers

Integral representation and embedding theorems for $n$-dimensional multianisotropic spaces with one anisotropic vertex

G. A. Karapetyan

Russian-Armenian (Slavonic) University, Yerevan, Armenia

Abstract: We prove embedding theorems for the multianisotropic Sobolev spaces generated by the completely regular Newton polyhedron. Under study is the case of the polyhedron with one anisotropic vertex. We obtain a special integral representation of functions in terms of the tuple of multi-indices of the Newton polyhedron.

Keywords: embedding theorems, multianisotropic space, completely regular polyhedron, integral representation.

UDC: 517.518.23

MSC: 35R30

Received: 23.06.2016

DOI: 10.17377/smzh.2017.58.308

 English version: Siberian Mathematical Journal, 2017, 58:3, 445–460

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