Aires E. M. Barbieri, José A. Gálvez, Yuanyuan Lian, Kai Zhang
We derive the asymptotic expansion at infinity for embedded ends of uniformly elliptic Weingarten surfaces with finite total curvature in $\mathbb{R}^3$, and we establish a maximum principle at infinity. Furthermore, we solve the Dirichlet problem for the uniformly elliptic Weingarten equation in dimension two on strictly convex bounded domains.
Aires E. M. Barbieri, José A. Gálvez, Yuanyuan Lian, Kai Zhang
This paper contains 7 sections, 24 theorems, 288 equations, 1 figure.
Theorem 1.1
Let $\Omega \subset \mathbb{R}^2$ be a strictly convex, bounded domain of class $C^{2,\alpha}$, and let $\varphi \in C^{2,\alpha}(\partial \Omega)$, with $0 < \alpha < 1$. Then there exists a unique solution $u \in C^{2,\beta}(\bar{\Omega})$ (for some $0 < \beta \leq \alpha$) to e1.6--e1.6-2--e1.6-t Moreover, where $C$ depends only on $\Lambda$, $\alpha$, $\max \kappa_{\partial \Omega}$, $\min \k
