# Embedding operators in Sobolev-Lions spaces and applications

## TL;DR

This paper investigates the embedding operators in Sobolev-Lions spaces, establishing their continuity and compactness, and applies these results to analyze degenerate anisotropic differential operators and related parabolic problems.

## Contribution

It introduces new results on the embedding operators in Sobolev-Lions spaces and applies them to degenerate anisotropic differential equations and parabolic problem estimates.

## Key findings

- Embedding operators are continuous and compact in Sobolev-Lions spaces.
- Separability properties of degenerate anisotropic differential operators are established.
- Well-posedness and Strichartz estimates for related parabolic problems are proven.

## Abstract

The continouity and compactness of embedding operators in in Sobolev-Lions type spaces are derived. By applying this result separability properties of degenerate anisotropic differential operator equations, well-posedeness and Strichartz type estimates for solution of corresponding parabolic problem are established