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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2509.08735 |
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| _version_ | 1866915510357065728 |
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| author | Müller, Marius |
| author_facet | Müller, Marius |
| contents | We prove optimal Lipschitz regularity for weak solutions of the measure-valued $p$-Poisson equation $-Δ_p u = Q \; \mathcal{H}^{n-1} \llcorner Γ$. Here $p \in (1,2)$, $Γ$ is a compact and connected $C^2$-hypersurface without boundary, and $Q$ is a positive $W^{2,\infty}$-density. This equation can be understood as a nonlinear interface transmission problem. Our main result extends previous studies of the linear case and provides further insights on a delicate limit case of (linear and nonlinear) potential theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz regularity for $p$-harmonic interface transmission problems Müller, Marius Analysis of PDEs We prove optimal Lipschitz regularity for weak solutions of the measure-valued $p$-Poisson equation $-Δ_p u = Q \; \mathcal{H}^{n-1} \llcorner Γ$. Here $p \in (1,2)$, $Γ$ is a compact and connected $C^2$-hypersurface without boundary, and $Q$ is a positive $W^{2,\infty}$-density. This equation can be understood as a nonlinear interface transmission problem. Our main result extends previous studies of the linear case and provides further insights on a delicate limit case of (linear and nonlinear) potential theory. |
| title | Lipschitz regularity for $p$-harmonic interface transmission problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.08735 |