On non-autonomous maximal regularity for elliptic operators in   divergence form
  We consider the Cauchy problem for non-autonomous forms inducing elliptic operators in divergence form with Dirichlet, Neumann, or mixed boundary conditions on an open subset $\Omega$ $\subseteq$ R n. We obtain maximal regularity in L 2 ($\Omega$) if the coefficients are bounded, uniformly elliptic, and satisfy a scale invariant bound on their fractional time-derivative of order one-half. Previous results even for such forms required control on a time-derivative of order larger than one-half. 
Pascal Auscher (LM-Orsay), Moritz Egert (LM-Orsay)
math.FA math.AP