On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients (Q2042893)

The paper deals with weak solutions to conormal derivative problem for linear, uniformly parabolic operators of the form \[ \partial_t u -\sum_{i,j=1}^nD_i\big( a^{ij}(x,t)D_ju+a^i(x,t)u\big)+\sum_{i=1}^n b^i(x,t)D_iu+c(x,t)u. \] The coefficients \(a^{ij}\) and \(a\) are supposed to have Dini mean oscillation while \(b^i\) and \(c\) belong to \(L^q\) with \(q>n+2.\) Assuming suitable Dini regularity of the boundary, the authors prove continuous differentiablity of the weak solutions up to the boundary.