  In this short note we derive, for bounded domains, an upper bound for a
Friedrichs type constant in a weighted Friedrichs type inequality. This upper
bound generalizes a well known upper bound of the Friedrichs constant. This
upper bound is also used to improve an upper bound of a Maxwell type constant
for convex domains in $\mathbb{R}^3$. A simple numerical application is also
given: we apply the main result in a posteriori error estimation for an
elliptic problem.
