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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.14183 |
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| _version_ | 1866909979250786304 |
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| author | Kijaczko, Michał |
| author_facet | Kijaczko, Michał |
| contents | In this paper we consider fractional Sobolev spaces equipped with weights being powers of the distance to the boundary of the domain. We prove the versions of Bourgain--Brezis--Mironescu and Maz'ya--Shaposhnikova asymptotic formulae for weighted fractional Gagliardo seminorms. For $p>1$ we also provide a nonlocal characterization of classical weighted Sobolev spaces with power weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14183 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotics of weighted Gagliardo seminorms Kijaczko, Michał Analysis of PDEs Primary 46E35, Secondary 35A15 In this paper we consider fractional Sobolev spaces equipped with weights being powers of the distance to the boundary of the domain. We prove the versions of Bourgain--Brezis--Mironescu and Maz'ya--Shaposhnikova asymptotic formulae for weighted fractional Gagliardo seminorms. For $p>1$ we also provide a nonlocal characterization of classical weighted Sobolev spaces with power weights. |
| title | Asymptotics of weighted Gagliardo seminorms |
| topic | Analysis of PDEs Primary 46E35, Secondary 35A15 |
| url | https://arxiv.org/abs/2305.14183 |