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) − a i j ( x ) ∂ i j u ( x ) + A | x | 2 u ( x ) = f ( x ) , in B , which lead to the existence and sharp regularity results of the classical solutions. More precisely, we prove that u ∈ C n + 2 , γ provided f ∈ C n , γ , a i j ∈ C n , γ and A > Λ ( 2 + n + γ ) ( d + n + γ ) .