The Das-Moser commutator closure for filtering through a boundary is well-posed

When filtering through a wall with constant averaging radius, in addition to the subfilter scale stresses, a non-closed commutator term arises. We consider a proposal of Das and Moser to close the commutator error term by embedding it in an optimization problem. This report shows that this optimization-based closure, with a small modification, leads to a well-posed problem showing the existence of a minimizer. We also derive the associated first order optimality conditions.