  Well-posedness \`a la Friedrichs is proved for a class of degenerate
Kolmogorov equations associated to stochastic Allen-Cahn equations with
logarithmic potential. The thermodynamical consistency of the model requires
the potential to be singular and the multiplicative noise coefficient to vanish
at the respective potential barriers, making thus the corresponding Kolmogorov
equation not uniformly elliptic in space. First, existence and uniqueness of
invariant measures and ergodicity are discussed. Then, classical solutions to
some regularised Kolmogorov equations are explicitly constructed. Eventually, a
sharp analysis of the blow-up rates of the regularised solutions and a passage
to the limit with a specific scaling yield existence \`a la Friedrichs for the
original Kolmogorov equation.
