Interior $C^{1,\alpha}$ regularity for infinity-harmonic functions

Proves uniform interior $C^{1,\alpha_d}$ regularity for bounded infinity-harmonic functions in every dimension d ≥ 3, for a positive exponent depending only on dimension. The gradient's supremum norm and Hölder seminorm on the half unit ball are bounded by a dimension-dependent constant times the oscillation on the unit ball. The exponent is not explicit.