  We consider the heat-kernel on a manifold whose boundary is piecewise smooth.
The set of independent geometrical quantities required to construct an
expression for the contribution of the boundary discontinuities to the C_{2}
heat-kernel coefficient is derived in the case of a scalar field with Dirichlet
and Robin boundary conditions. The coefficient is then determined using
conformal symmetry and evaluation on some specific manifolds. For the Robin
case a perturbation technique is also developed and employed. The contributions
to the smeared heat-kernel coefficient and cocycle function are calculated.
Some incomplete results for spinor fields with mixed conditions are also
presented.
