  In this note, we first introduce a boundary problem for Lagrangian
submanifolds, analogous to the problem for free boundary hypersurfaces and
capillary hypersurfaces. Then we present several interesting examples of
Lagrangian submanifolds satisfying this boundary condition and we prove a
Lagrangian version of Nitsche (or Hopf) type theorem. Some problems are
proposed at the end of this note.
