  Higher dimensional Euclidean Liouville conformal field theories (LCFTs)
consist of a log-correlated real scalar field with a background charge and an
exponential potential. We analyse the LCFT on a four-dimensional manifold with
a boundary. We extend to the boundary, the conformally covariant GJMS operator
and the ${\cal Q}$-curvature term in the LCFT action and classify the conformal
boundary conditions. Working on a flat space with plate boundary, we calculate
the dimensions of the boundary conformal primary operators, the two- and
three-point functions of the displacement operator and the boundary conformal
anomaly coefficients.
