Exact constants in Poincare type inequalities for functions with zero mean boundary traces
Analysis of PDEs
2015-02-24 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1211.2224,
title = {Exact constants in Poincare type inequalities for functions with zero mean boundary traces},
author = {Alexander I. Nazarov and Sergey I. Repin},
journal= {arXiv preprint arXiv:1211.2224},
year = {2015}
}
Comments
A gap in the proof of Theorem 3.2 is fixed; 19 pages, 3 figures