A remark on optimal weighted Poincar\'e inequalities for convex domains

By V. Ferone, Carlo Nitsch, Cristina Trombetti. 2012

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

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e5f4f9a027c5201933e294327066ba72caeab4c1