Schauder estimates of the uniformly elliptic equation with a inverse-square potential

In this paper, we derive Schauder estimates to the solutions of the following uniformly elliptic equation with a inverse-square potential and nonhomogeneous term(0.1)−aij(x)∂iju(x)+A|x|2u(x)=f(x),in B, which lead to the existence and sharp regularity results of the classical solutions. More precisely, we prove that u∈Cn+2,γ provided f∈Cn,γ, aij∈Cn,γ and A>Λ(2+n+γ)(d+n+γ).