  We show local well-posedness for the Mullins-Sekerka system with ninety
degree angle boundary contact. We will describe the motion of the moving
interface by a height function over a fixed reference surface. Using the theory
of maximal regularity together with a linearization of the equations and a
localization argument we will prove well-posedness of the full nonlinear
problem via the contraction mapping principle. Here one difficulty lies in
choosing the right space for the Neumann trace of the height function and
showing maximal $L_p-L_q$-regularity for the linear problem.
  In the second part we show that solutions starting close to certain
equilibria exist globally in time, are stable, and converge to an equilibrium
solution at an exponential rate.
