  We consider the problem of conditioning the Brownian excursion to have a
fixed time average over the interval [0,1] and we study an associated
stochastic partial differential equation with reflection at 0 and with the
constraint of conservation of the space average. The equation is driven by the
derivative in space of a space-time white noise and contains a double Laplacian
in the drift. Due to the lack of the maximum principle for the double
Laplacian, the standard techniques based on the penalization method do not
yield existence of a solution.
