On non-autonomous maximal regularity for elliptic operators in\n divergence form

Abstract

We consider the Cauchy problem for non-autonomous forms inducing elliptic\noperators in divergence form with Dirichlet, Neumann, or mixed boundary\nconditions on an open subset $\\Omega$ $\\subseteq$ R n. We obtain maximal\nregularity in L 2 ($\\Omega$) if the coefficients are bounded, uniformly\nelliptic, and satisfy a scale invariant bound on their fractional\ntime-derivative of order one-half. Previous results even for such forms\nrequired control on a time-derivative of order larger than one-half.\n