  In the paper, we investigate Poincare type inequalities for the functions
having zero mean value on the whole boundary of a Lipschitz domain or on a
measurable part of the boundary. We derive exact and easily computable
constants for some basic domains (rectangles, cubes, and right triangles). In
the last section, we derive an a estimate of the difference between the exact
solutions of two boundary value problems. Constants in Poincare type
inequalities enter these estimates, which provide guaranteed a posteriori error
control.
