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Let $u\\in C^0(\\Omega)$ be a viscosity solution to the inhomogeneous $\\infty$-Laplace equation $$ -\\Delta_{\\infty} u :=-\\frac12\\sum_{i=1}^2(|Du|^2)_iu_i= -\\sum_{i,j=1}^2u_iu_ju_{ij} =f \\quad {\\rm in}\\ \\Omega. $$ The following are proved in this paper.\n  (i) For $ \\alpha > 3/2$, we have $|Du|^{\\alpha}\\in W^{1,2}_{loc}(\\Omega)$, which is (asymptotic) sharp when $ \\alpha \\to 3/2$. 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