Optimal global regularity for minimal graphs over convex domains in hyperbolic space

摘要

Abstract We use the concept of the inside-(a, η, h) domain to construct a subsolution to the Dirichlet problem for minimal graphs over convex domains in hyperbolic space. As an application, we prove that the H?lder exponent max{1/a, 1/(n + 1)} for the problem is optimal for any a ∈ [2, +∞].