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We show that a viscosity solution of a uniformly elliptic, fully nonlinear equation which vanishes on an open set must be identically zero, provided that the equation is C 1,1 . We do not assume that the nonlinearity is convex or concave, and thus a priori C 2 estimates are unavailable. Nevertheless, we use the boundary Harnack inequality and a regularity result for solutions with small oscillations to prove that the solution must be smooth at an appropriate point on the boundary of the set ondoi:10.4310/mrl.2011.v18.n5.a9 fatcat:kjy5mw65vngj3bvbrvlalrgvs4