Embeddings of a Multi-Weighted Anisotropic Sobolev Type Space

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.