A boundary value problem is commonly associated with constraints imposed on a
system at its boundary. We advance here an alternative point of view treating
the system as interacting "boundary" and "interior" subsystems. This view is
implemented through a Lagrangian framework that allows to account for (i) a
variety of forces including dissipative acting at the boundary; (ii) a
multitude of features of interactions between the boundary and the interior
fields when the boundary fields may differ from the boundary limit of the
interior fields; (iii) detailed pictures of the energy distribution and its
flow; (iv) linear and nonlinear effects. We provide a number of elucidating
examples of the structured boundary and its interactions with the system
interior. We also show that the proposed approach covers the well known
boundary value problems.Comment: 41 pages, 3 figure
