Elliptic equations with singular BMO coefficients in Reifenberg domains

AbstractW1,p estimate for the solutions of elliptic equations whose coefficient matrix can have large jump along the boundary of subdomains is obtained. The principal coefficients are supposed to be in the John–Nirenberg space with small BMO seminorms, and the domain and subdomains are Reifenberg flat domains. Moreover, it has been shown that the estimates are uniform with respect to the distance between the subdomains