L. D’Onofrio

Regularity for Elliptic Equations with Coefficients of Small Mean Oscillation

We give a detailed proof of interior $W^{2,p}$ regularity for uniformly elliptic equations in nondivergence form \[ a^{ij}(x)D_{ij}u+b^i(x)D_i u=f. \] The leading matrix is assumed to have sufficiently small mean oscillation on the balls under consideration. The proof uses a modern real-variable argument: a constant-co...