  We study boundary value problems for the Dirac operator on Riemannian
Spin$^c$ manifolds of bounded geometry and with noncompact boundary. This
generalizes a part of the theory of boundary value problems by C. B\"ar and W.
Ballmann for complete manifolds with closed boundary. As an application, we
derive the lower bound of Hijazi-Montiel-Zhang, involving the mean curvature of
the boundary, for the spectrum of the Dirac operator on the noncompact boundary
of a Spin$^c$ manifold. The limiting case is then studied and examples are then
given.
