Hölder Estimates for the Homogenization of a Curl–Div System Related to Maxwell’s Equations With VMO Coefficients

In this paper, we consider the curl–div system: ∇×( A ( x / ε )∇× u _ε ) = ∇× f and ∇⋅ u _ε = 0 with rapidly oscillating periodic coefficients. This system is related to Maxwell’s equations and has a structure different from that of general elliptic systems. Under VMO coefficients, we establish the uniform interior Hölder estimates and local boundary Hölder estimates for u _ε . All estimates for u _ε are independent of ε .