Removable singular sets for equations of the formsum {tfrac{partial }{{partial x_i }}a_{ij} (x)tfrac{{partial u}}{{partial x_j }} = f(x,u,nabla u)}

The following uniformly elliptic equation is considered: $$sum {tfrac{partial }{{partial x_i }}a_{ij} (x)tfrac{{partial u}}{{partial x_j }} = f(x,u,nabla u)} , x in Omega subset R^n ,$$ with measurable coefficients. The function f satisfies the condition $$f(x, u, nabla u) u geqslant C|u|^{beta _1 + 1} |nabla u|^{beta _1 } , beta _1 > 0, 0 leqslant beta _2 leqslant 2, beta _1 + beta _2 > 1$$ . It is proved that if u(x) is a generalized (in the sense of integral identity) solution in the domain ΩK, where the compactum K has Hausdorff dimension α, and if (frac{{2beta _1 + beta _2 }}{{beta _1 + beta _2 - 1}}< n - alpha ) , u(x) will be a generalized solution in the domain ω. Moreover, the sufficient removability conditions for the singular set are, in some sense, close to the necessary conditions.