Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912706563407872 |
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| author | Azzam, Jonas Mourgoglou, Mihalis Villa, Michele |
| author_facet | Azzam, Jonas Mourgoglou, Mihalis Villa, Michele |
| contents | Given a corkscrew domain with uniformly rectifiable boundary, we construct a surjective trace map onto the $L^p$ Hajlasz-Sobolev space on the boundary from the space of functions on the domain with $L^p$ norm involving the non-tangential maximal function of the gradient and the conical square function of the Hessian. This fundametally uses the Dorronsoro theorem for UR sets proven in a companion paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_10137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries Azzam, Jonas Mourgoglou, Mihalis Villa, Michele Classical Analysis and ODEs 46E35 Given a corkscrew domain with uniformly rectifiable boundary, we construct a surjective trace map onto the $L^p$ Hajlasz-Sobolev space on the boundary from the space of functions on the domain with $L^p$ norm involving the non-tangential maximal function of the gradient and the conical square function of the Hessian. This fundametally uses the Dorronsoro theorem for UR sets proven in a companion paper. |
| title | Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries |
| topic | Classical Analysis and ODEs 46E35 |
| url | https://arxiv.org/abs/2511.10137 |