Liouville conformal field theory (LCFT) is considered on a simply connected domain with boundary, specializing to the case where potential integrated only over boundary of domain. We work in probabilistic framework LCFT introduced by Huang et al. (Ann Inst H Poincare Probab Statist 54(3):1694–1730, 2018. https://doi.org/10.1214/17-AIHP852 ). Building upon known proof bulk one-point function fir...