Sharp Constants in the ”Boundary” Poincaré Inequality

A.I. Nazarov

St.-Petersburg Dept of Steklov Institute and St.-Petersburg State University, Russia

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). We also discuss an application of those inequalities to quantitative analysis of partial differential equations. The talk is based on the joint work with Sergey Repin (St.-Petersburg Dept of Steklov Institute and University of Jyväskylä, Finland).