Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Müller, Marius
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416256245
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