  We study the c_L=25 limit, which corresponds to c=1 string theory, of bulk
and boundary correlation functions of Liouville theory with FZZT boundary
conditions. This limit is singular and requires a renormalization of vertex
operators. We formulate a regularization procedure which allows to extract
finite physical results. A particular attention is paid to c=1 string theory
compactified at the self-dual radius R=1. In this case, the boundary
correlation functions diverge even after the multiplicative renormalization. We
show that all infinite contributions can be interpreted as contact terms
arising from degenerate world sheet configurations. After their subtraction,
one gets a well defined set of correlation functions. We also obtain several
new results for correlation functions in Liouville theory at generic central
charge.
