Lorentz estimate for nonlinear parabolic obstacle problems with asymptotically regular nonlinearities

In this paper, we mainly prove an interior Lorentz estimate of the spatial gradient of weak solutions to a class of nonlinear parabolic problems with an irregular obstacle in a bounded cylindrical domain when the nonlinearity is merely asymptotically regular. We assume that the associated nonlinearity satisfies certain ellipticity and growth conditions and the (δ,R)(δ,R)-vanishing condition. Here, the approach of constructing a regular obstacle problem via Poisson’s formula is used to establish Lorentz estimate for such an asymptotically regular obstacle problem.