Calderon-Zygmund type estimates for singular quasilinear elliptic obstacle problems with measure data

We establish a Calderon-Zygmund type estimate for elliptic obstacle prob-lems of p-Laplace type involving measure data under fractional maximal functions. Here, the problem is considered for the singular case when 1 < p & LE; 2 - 1/n and we prove the global regularity for weak solutions in the Lorentz spaces setting, under the assumption of small BMO coefficients and the domain being sufficiently fiat in Reifenberg's sense.