  Liouville conformal field theory is considered with conformal boundary. There
is a family of conformal boundary conditions parameterized by the boundary
cosmological constant, so that observables depend on the dimensional ratios of
boundary and bulk cosmological constants. The disk geometry is considered. We
present an explicit expression for the expectation value of a bulk operator
inside the disk and for the two-point function of boundary operators. We
comment also on the properties of the degenrate boundary operators. Possible
applications and further developments are discussed. In particular, we present
exact expectation values of the boundary operators in the boundary sin-Gordon
model.
