Global weighted Lorentz estimates to nonlinear parabolic equations over nonsmooth domains

An elaborate method is developed to establish a global Calderón-Zygmund type theory in weighted Lorentz spaces Lω(γ,q)(ΩT) for zero Cauchy-Dirichlet problem of nonlinear parabolic equations of p-Laplacian type with p>2dd+2. Here, we assume that the nonlinearity a=a(t,x,ξ) is merely measurable in the time variable t, and has a mall BMO semi-norm in the spatial variables x uniformly in ξ variables, while the boundary ∂Ω of bounded domain Ω is flat in the sense of Reifenberg. Our result not only develops nonlinear Calderón-Zygmund theory under weak regularity assumptions on the datum, but also extends the related framework from Lebesgue spaces to refined weighted Lorentz spaces.