Abstract
Let Ω ⊂ R n be a bounded domain of class C 2 + α , 0 < α < 1 . We show that if n ⩾ 3 and u Ω is the maximal solution of equation Δ u = n ( n - 2 ) u ( n + 2 ) / ( n - 2 ) in Ω , then the hyperbolic radius v Ω = u Ω - 2 / ( n - 2 ) is of class C 2 + α up to the boundary. The argument rests on a reduction to a nonlinear Fuchsian elliptic PDE.
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