The following uniformly elliptic equation is considered: [GRAPHICS] with measurable coefficients. The function f satisfies the condition f(x, u, delu)u greater-than-or-equal-to C\u\beta1+1\delu\beta2, beta1>0, 0 less-than-or-equal-to beta2 less-than-or-equal-to 2, beta1+beta2>1. It is proved that if u(x) is a generalized (in the sense of integral identity) solution in the domain OMEGA\K, where the compactum K has Hausdorff dimension alpha, and if 2beta1+beta2/beta1+beta2-1<n-alpha, u(x) will be a generalized solution in the domain OMEGA. Moreover, the sufficient removability conditions for the singular set are, in some sense, close to the necessary conditions.
