Abstract:
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.
