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| Natura: | Preprint |
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2022
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| Accesso online: | https://arxiv.org/abs/2212.07788 |
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| _version_ | 1866912127374065664 |
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| author | Gol'dshtein, Vladimir Ukhlov, Alexander |
| author_facet | Gol'dshtein, Vladimir Ukhlov, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07788 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometric theory of composition operators on Sobolev spaces Gol'dshtein, Vladimir Ukhlov, Alexander Analysis of PDEs 46E35, 30C65 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. |
| title | Geometric theory of composition operators on Sobolev spaces |
| topic | Analysis of PDEs 46E35, 30C65 |
| url | https://arxiv.org/abs/2212.07788 |