A remark on optimal weighted Poincaré inequalities for convex domains

Abstract

We prove a sharp upper bound on convex domains, in terms of the diameter alone, of the best constant in a class of weighted Poincaré inequalities. The key point is the study of an optimal weighted Wirtinger inequality.

Few typos have been corrected. 10 pages. No figures. arXiv admin note: substantial text overlap with arXiv:1110.2960