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In the paper, we investigate Poincare type inequalities for the functionshaving zero mean value on the whole boundary of a Lipschitz domain or on ameasurable part of the boundary. We derive exact and easily computableconstants for some basic domains (rectangles, cubes, and right triangles). Inthe last section, we derive an a estimate of the difference between the exactsolutions of two boundary value problems. Constants in Poincare typeinequalities enter these estimates, which provide guaranteed a posteriori errorcontrol.

Exact constants in Poincare type inequalities for functions with zero mean boundary traces