Weighted estimates for nondivergence parabolic equations in Orlicz spaces (Q490723)

The authors prove global weighted Orlicz regularity for the higher-order derivatives of solutions to Cauchy-Dirichlet problem for nondivergence parabolic equations of the form \[ \begin{cases} u_t-a_{ij}(x,t)D_{ij}u=f(x,t) & \text{in }\Omega_T=\Omega\times(0,T),\\ u(x,t)=0 & \text{on }\partial_p \Omega_T, \end{cases} \] with a bounded and \(C^{1,1}\)-smooth domain \(\Omega\). The coefficients \(a_{ij}(x,t)\) are assumed to have small bounded mean oscillation (BMO) seminorms.