Extensions of traces for Sobolev mappings into manifolds at the endpoint $p=1$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916627844431872 |
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| author | Van Schaftingen, Jean Van Vaerenbergh, Benoît |
| author_facet | Van Schaftingen, Jean Van Vaerenbergh, Benoît |
| contents | We give direct proofs and constructions of the trace and extension theorems for Sobolev mappings in $W^{1, 1} (M, N)$, where $M$ is Riemannian manifold with compact boundary $\partial M$ and $N$ is a complete Riemannian manifold. The analysis is also applicable to halfspaces and strips. The extension is based on a tiling the domain of the considered applications by suitably chosen dyadic cubes to construct the desired extension. Along the way, we obtain asymptotic characterizations of the $L^1$-energy of mappings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions of traces for Sobolev mappings into manifolds at the endpoint $p=1$ Van Schaftingen, Jean Van Vaerenbergh, Benoît Analysis of PDEs Functional Analysis 58D15 (Primary) 46E35, 46T10, 58J32 (Secondary) We give direct proofs and constructions of the trace and extension theorems for Sobolev mappings in $W^{1, 1} (M, N)$, where $M$ is Riemannian manifold with compact boundary $\partial M$ and $N$ is a complete Riemannian manifold. The analysis is also applicable to halfspaces and strips. The extension is based on a tiling the domain of the considered applications by suitably chosen dyadic cubes to construct the desired extension. Along the way, we obtain asymptotic characterizations of the $L^1$-energy of mappings. |
| title | Extensions of traces for Sobolev mappings into manifolds at the endpoint $p=1$ |
| topic | Analysis of PDEs Functional Analysis 58D15 (Primary) 46E35, 46T10, 58J32 (Secondary) |
| url | https://arxiv.org/abs/2502.17245 |