Regularity estimates for singular parabolic measure data problems with sharp growth

We prove global gradient estimates for parabolic p-Laplace type equations with measure data, whose model isut−div(|Du|p−2Du)=μinΩ×(0,T)⊂Rn×R,where μ is a signed Radon finite total mass. consider the singular case2nn+1<p≤2−1n+1and give possibly minimal conditions on nonlinearity and boundary of Ω, which guarantee regularity results such data problems.