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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2509.08735 |
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- 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.