  We study the short-time existence and regularity of solutions to a boundary
value problem for the Ricci-DeTurck equation on a manifold with boundary. Using
this, we prove the short-time existence and uniqueness of the Ricci flow
prescribing the mean curvature and conformal class of the boundary, with
arbitrary initial data. Finally, we establish that under suitable control of
the boundary data the flow exists as long as the ambient curvature and the
second fundamental form of the boundary remain bounded.
