Qing Han, Weiming Shen, Yue Wang
Published 2015-11-03Version 1
We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $\Omega\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal regularity $f\in C^{\frac{1}{n+1}}(\bar{\Omega})$. We can improve the H\"older exponent for $f$ if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.
Comments: Accepted by Calc. Var. Partial Differential Equations
Perturbations of the Dirichlet Problem and Error Bounds
The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients in a wedge
The $L^p$ Dirichlet Problem for the Stokes System on Lipschitz Domains
![QR code for arXiv:1511.01143 [math.AP]](http://oss.arxitics.com/images/favicon.svg)