Global Calderón-Zygmund L2-theory for anisotropic parabolic problems

We establish the global Calderón-Zygmund L2-estimate for solutions to Cauchy-Dirichlet problem of anisotropic parabolic equations, where the forcing term is square-integrable and the initial data belongs to an Orlicz-Sobolev space. Our findings broaden the established regularity result for nonlinear parabolic equations of the p-Laplacian type, as demonstrated by Cianchi-Maz’ya (2020). Minimal regularity on the boundary of the domain is required, although our result is new even for smooth domains. Additionally, our conclusion holds for all bounded convex domains.