Embeddings of a Multi-Weighted Anisotropic Sobolev Type Space
Соболев типтi көпсалмақты анизотроптық кеңiстiктiң енгiзулерi
Вложения многовесового анизотропного пространства типа Соболева
Iskakova G.Sh Aitenova M.S. Sexenbayeva A.K.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#113Issue 173 - 83 pp.
Parameters such as various integral and differential characteristics of functions, smoothness properties of regions and their boundaries, as well as many classes of weight functions cause complex relationships and embedding conditions for multi-weighted anisotropic Sobolev type spaces. The desire not to restrict these parameters leads to the development of new approaches based on the introduction of alternative definitions of spaces and norms in them or on special localization methods. This article examines the embeddings of multi-weighted anisotropic Sobolev type spaces with anisotropy in all the defining characteristics of the norm of space, including differential indices, summability indices, as well as weight coefficients. The applied localization method made it possible to obtain an embedding for the case of an arbitrary domain and weights of a general type, which is important in applications in differential operators’ theory, numerical analysis.
Anisotropic Sobolev Spaces , Embedding Theorems , Localization Methods , Multi-Weighted Spaces , Weighted Functions
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Karaganda Buketov University, Karaganda, Kazakhstan
Karaganda University of Kazpotrebsoyuz, Karaganda, Kazakhstan
Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan
L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Karaganda Buketov University
Karaganda University of Kazpotrebsoyuz
Kazakhstan Branch of Lomonosov Moscow State University
L.N. Gumilyov Eurasian National University
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