Geometric theory of composition operators on Sobolev spaces
Analysis of PDEs
2024-11-21 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2212.07788,
title = {Geometric theory of composition operators on Sobolev spaces},
author = {Vladimir Gol'dshtein and Alexander Ukhlov},
journal= {arXiv preprint arXiv:2212.07788},
year = {2024}
}
Comments
33 pages. arXiv admin note: text overlap with arXiv:2207.07541