Year: 2026
Type: preprint
Abstract: We prove that the capillary $L_p$ dual Minkowski problem in $\mathbb{R}^{n+1}$, $n\geq3$, admits a unique positive smooth strictly convex solution for any prescribed positive smooth function $f$ when $p>q$ and the contact angle satisfies $θ\in(0,π/2)$. Earlier results for $p>q$ either required the additional condition $q\leq1$ or were restricted to $n=2$. We reduce the problem to a Monge--Ampère type equation with a Robin boundary condition on a spherical cap. By constructing a new auxiliary function for the global $C^2$ estimate, we overcome these limitations and completely resolve the case of $p>q$ in higher dimensions, i.e., prove existence and uniqueness throughout the case of $p>q$, without any further restriction on $p$ or $q$.
Source: arXiv (Cornell University)
Author: Gao, Ya
Institution: South Central Minzu University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212051130