  We establish an explicit $L^\infty(\Om)$ a priori estimate for weak solutions
to subcritical elliptic problems with nonlinearity on the boundary, in terms of
the powers of their $H^1(\Om)$ norms. To prove our result, we combine in a
novel way Moser type estimates together with elliptic regularity and
Gagliardo--Nirenberg interpolation inequality. We illustrate our result with an
application to subcritical problems satisfying Ambrosetti-Rabinowitz condition.
