  In the decoupling limit of DGP, Pi describes the brane-bending degree of
freedom. It obeys second order equations of motion, yet it is governed by a
higher derivative Lagrangian. We show that, analogously to the Einstein-Hilbert
action for GR, the Pi-Lagrangian requires Gibbons-Hawking-York type boundary
terms to render the variational principle well-posed. These terms are important
if there are other boundaries present besides the DGP brane, such as in higher
dimensional cascading DGP models. We derive the necessary boundary terms in two
ways. First, we derive them directly from the brane-localized Pi-Lagrangian by
demanding well-posedness of the action. Second, we calculate them directly from
the bulk, taking into account the Gibbons-Hawking-York terms in the bulk
Einstein-Hilbert action. As an application, we use the new boundary terms to
derive Israel junction conditions for Pi across a sheet-like source. In
addition, we calculate boundary terms and junction conditions for the galileons
which generalize the DGP Pi-lagrangian, showing that the boundary term for the
n-th order galileon is the (n-1)-th order galileon.
