$L^p$-solvability of boundary value problems for the Laplacian in locally flat unbounded domains
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912364309250048 |
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| author | Guillén-Mola, Ignasi |
| author_facet | Guillén-Mola, Ignasi |
| contents | We establish the solvability of the $L^p$-Dirichlet and $L^{p^\prime}$-Neumann problems for the Laplacian for $p\in (\frac{n}{n-1}-\varepsilon,\frac{2n}{n-1}]$ for some $\varepsilon>0$ in $2$-sided chord-arc domains with unbounded boundary that is sufficiently flat at large scales and outward unit normal vector whose oscillation fails to be small only at finitely many dyadic boundary balls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^p$-solvability of boundary value problems for the Laplacian in locally flat unbounded domains Guillén-Mola, Ignasi Analysis of PDEs Classical Analysis and ODEs Functional Analysis 31B10, 35B30, 35J25, 42B20. Secondary: 31B05, 42B37 We establish the solvability of the $L^p$-Dirichlet and $L^{p^\prime}$-Neumann problems for the Laplacian for $p\in (\frac{n}{n-1}-\varepsilon,\frac{2n}{n-1}]$ for some $\varepsilon>0$ in $2$-sided chord-arc domains with unbounded boundary that is sufficiently flat at large scales and outward unit normal vector whose oscillation fails to be small only at finitely many dyadic boundary balls. |
| title | $L^p$-solvability of boundary value problems for the Laplacian in locally flat unbounded domains |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis 31B10, 35B30, 35J25, 42B20. Secondary: 31B05, 42B37 |
| url | https://arxiv.org/abs/2503.23865 |