Consider the nonlinear parabolic equation in the form ut − diva(Du, x, t) = div (|F|p−2F) in Ω × (0, T ), where T > 0 and Ω is a Reifenberg domain. We suppose that the nonlinearity a(ξ, x, t) has a small BMO norm with respect to x and is merely measurable and bounded with respect to the time variable t. In this paper, we prove the global Calderón-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calderón-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity a(ξ, x, t) and to more general setting of Lorentz spaces.
|Number of pages||24|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2017|