Non-Autonomous Maximal Regularity for Forms Given by Elliptic Operators   of Bounded Variation
  We show maximal $L^p$-regularity for non-autonomous Cauchy problems provided the trace spaces are stable in some parameterized sense and the time dependence is of bounded variation. In particular, on $L^2$, we obtain for all $p \in (1,2]$ maximal $L^p$-regularity for non-autonomous elliptic operators with measurable coefficients. 
Stephan Fackler
math.FA math.AP