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

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 Hölder exponent \max \{1/a,1/(n+1)\} for the problem is optimal for any a\in [2,+\infty ].

Key words： Minimal graph equation; optimal regularity; global regularity

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