Exact constants in Poincaré type inequalities for functions with zero mean boundary traces
Alexander Il'ich Nazarov, Sergey Igorevich Repin · Mathematical Methods in the Applied Sciences · 2014
In this paper, we investigate Poincaré 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 find exact and easily computable constants in these inequalities for some basic domains (rectangles, cubes, and right triangles) and discuss applications of the inequalities to quantitative analysis of partial differential equations. Copyright © 2014 John Wiley & Sons, Ltd.