(untitled) (Journal of Partial Differential Equations, 2018)
Recently R. Jensen [1] has proved the uniqueness of viscosity solutions in W^1,&#8734 of second order fully nonlinear elliptic equation F (D&sup2, Du, u) = 0. He does not assume F to be convex. In this paper we extend his result [1] to the case that F can be dependent on x, i. e. prove that the viscosity solutions in W^1,&#8734 of the second order fully nonlinear elliptic equation F (D&sup2u, Du, u, x) = 0 are unlique. We do not assume F to be convex either.