Conditional C^{1,gamma} regularity for any gamma in (0,1) is proved for strong W^{2,n}_{loc} solutions of the linearized Monge-Ampere obstacle problem.
Caffarelli,Interior W 2,p estimates for solutions of the Monge-Ampère equation, Annals of Mathematics 131 (1990), no
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$C^{1,\alpha}$ regularity of the solution for the obstacle problem for the linearized Monge-Amp\`ere operator
Conditional C^{1,gamma} regularity for any gamma in (0,1) is proved for strong W^{2,n}_{loc} solutions of the linearized Monge-Ampere obstacle problem.