A Remark on the Sobolev Regularity of Classical Solutions of Strongly Elliptic Equations

We prove that C 2,α ( Ω ) solutions of problem (1.2) below are in H m+2 (Ω) for all m ∈ ℕ, if f and the coefficients are in H m (Ω) n C 0,α ( Ω ) Previously, this result was explicitly known only if m > n /2 (or if m = 0). A similar result holds for the quasi‐linear equation (1.11) below.