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In this paper, we can obtain curvature estimates for spacelike admissiblegraphic hypersurfaces in the $(n+1)$-dimensional Lorentz-Minkowski space$\mathbb{R}^{n+1}_{1}$, and through which the existence of spacelike admissiblegraphic hypersurfaces, with prescribed $2$-th Weingarten curvature andDirichlet boundary data, defined over a strictly convex domain in thehyperbolic plane $\mathscr{H}^{n}(1)\subset\mathbb{R}^{n+1}_{1}$ of center atorigin and radius $1$, can be proven.

Curvature estimates for spacelike graphic hypersurfaces in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$