Entropic repulsion of the massless field with a class of self-potentials

We consider the d+1-dimensional effective interface model of gradient type with a quadratic interaction potential and a self-potential. Without the self-potential, the model coincides with the d-dimensional massless Gaussian field. We show that for an arbitrary repulsive self-potential which can be thought as interaction of the interface with a "soft wall", the field is pushed up at least to the same level when the original Gaussian field is conditioned to be positive everywhere, namely the "hard wall" condition is imposed.