2023/10/12 by Fa Peng, Peng, Fa, Yi Ru-Ya Zhang +3 · 1 citation
Computer Science · Mathematics · #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2310.08093
openalex publication_date 2023/10/12 · openalex created_date 2023/10/14 · openalex updated_date 2026/07/28
The exploration of shape metamorphism, surface reconstruction, and image interpolation raises fundamental inquiries concerning the C1 and higher-order regularity of ∞-harmonic potentials -- a specialized category of ∞-harmonic functions. Additionally, it prompts questions regarding their corresponding approximations using p-harmonic potentials. It is worth noting that establishing C1 and higher-order regularity for ∞-harmonic functions remains a central concern within the realm of ∞-Laplace equations and L^∞-variational problems. In this study, we investigate the regularity properties from p-harmonic potentials to ∞-harmonic potentials within arbitrary convex ring domains Ω=Ω0\backslash Ω1 in \mathbb Rn. Here Ω0 is a bounded convex domain in \mathbb Rn and Ω1⊂ Ω0 is a compact convex set. We prove the interior C1 and some Sobolev regularity for ∞-harmonic potentials.