2022/12/15 by Vladimir Gol’dshtein, Alexander Ukhlov, Gol'dshtein, Vladimir +1 · 1 citation
Computer Science · Engineering · Mathematics · #30C65 #46E35 #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #Elasticity and Wave Propagation #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2212.07788
openalex publication_date 2022/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present the basic concepts of the geometric theory of composition operators on Sobolev spaces. The main objects of the theory are topological mappings which generate bounded embedding operators on Sobolev spaces by the composition rule. This theory is in some sense a "generalization" of the theory of quasiconformal mappings, but the theory of composition operators is oriented to its applications to the Sobolev embedding theorems, the spectral theory of elliptic operators and continuum mechanics problems.