Lipschitz regularity for p-harmonic interface transmission problems

2025/09/10 by Marius Müller, Müller, Marius
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2509.08735

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove optimal Lipschitz regularity for weak solutions of the measure-valued p-Poisson equation -Δ_p u = Q H^n-1 \llcorner Γ. Here p ∈ (1,2), Γ is a compact and connected C²-hypersurface without boundary, and Q is a positive W^2,∞-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.

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