Complex interpolation of power-weighted Sobolev spaces with boundary conditions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915814912819200 |
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| author | Roodenburg, Floris B. |
| author_facet | Roodenburg, Floris B. |
| contents | We characterise the complex interpolation spaces of weighted vector-valued Sobolev spaces with and without boundary conditions on the half-space and on smooth bounded domains. The weights we consider are power weights that measure the distance to the boundary and do not necessarily belong to the class of Muckenhoupt $A_p$ weights. First, we determine the higher-order trace spaces for weighted vector-valued Besov, Triebel-Lizorkin, Bessel potential and Sobolev spaces. This allows us to derive a trace theorem for boundary operators and to interpolate spaces with boundary conditions. Furthermore, we derive density results for weighted Sobolev spaces with boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14636 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complex interpolation of power-weighted Sobolev spaces with boundary conditions Roodenburg, Floris B. Functional Analysis Analysis of PDEs Primary: 46B70, 46E35, Secondary: 46E40 We characterise the complex interpolation spaces of weighted vector-valued Sobolev spaces with and without boundary conditions on the half-space and on smooth bounded domains. The weights we consider are power weights that measure the distance to the boundary and do not necessarily belong to the class of Muckenhoupt $A_p$ weights. First, we determine the higher-order trace spaces for weighted vector-valued Besov, Triebel-Lizorkin, Bessel potential and Sobolev spaces. This allows us to derive a trace theorem for boundary operators and to interpolate spaces with boundary conditions. Furthermore, we derive density results for weighted Sobolev spaces with boundary conditions. |
| title | Complex interpolation of power-weighted Sobolev spaces with boundary conditions |
| topic | Functional Analysis Analysis of PDEs Primary: 46B70, 46E35, Secondary: 46E40 |
| url | https://arxiv.org/abs/2503.14636 |