Compactness of weighted Sobolev trace operators and non-linear Steklov problems
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914524902195200 |
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| author | Menovschikov, Alexander Ukhlov, Alexander |
| author_facet | Menovschikov, Alexander Ukhlov, Alexander |
| contents | We prove the compactness of weighted Sobolev trace operators in outward cuspidal domains by using composition operators on Sobolev spaces. This result allows us to formulate the non-linear Steklov problem in outward cuspidal domains in a correct functional setting and to establish the existence of its non-trivial solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00795 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compactness of weighted Sobolev trace operators and non-linear Steklov problems Menovschikov, Alexander Ukhlov, Alexander Analysis of PDEs 46E35, 30C65, 35P30 We prove the compactness of weighted Sobolev trace operators in outward cuspidal domains by using composition operators on Sobolev spaces. This result allows us to formulate the non-linear Steklov problem in outward cuspidal domains in a correct functional setting and to establish the existence of its non-trivial solution. |
| title | Compactness of weighted Sobolev trace operators and non-linear Steklov problems |
| topic | Analysis of PDEs 46E35, 30C65, 35P30 |
| url | https://arxiv.org/abs/2605.00795 |