  Mesoscopic theory for self-assembling systems near a planar confining surface
is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC)
for the local volume fraction and the correlation function are derived from the
DFT expression for the grand thermodynamic potential. Various levels of
approximation can be considered for the obtained equations. The lowest-order
nontrivial approximation (GM) resembles the Landau-Brazovskii type theory for a
semiinfinite system. Unlike in the original phenomenological theory, however,
all coefficients in our equations and BC are expressed in terms of the
interaction potential and the thermodynamic state. Analytical solutions of the
linearized equations in GM are presented and discussed on a general level and
for a particular example of the double-Yukawa potential. We show exponentially
damped oscillations of the volume fraction and the correlation function in the
direction perpendicular to the confining surface. The correlations show
oscillatory decay in directions parallel to this surface too, with the decay
length increasing significantly when the system boundary is approached. The
framework of our theory allows for a systematic improvement of the accuracy of
the results.
