Best constants in Poincaré inequalities for convex domains
By L. Esposito, Carlo Nitsch, Cristina Trombetti. 2011
67 citations recorded by the source corpus.
We prove a Payne-Weinberger type inequality for the $p$-Laplacian Neumann eigenvalues ($p\ge 2$). The inequality provides the sharp upper bound on convex domains, in terms of the diameter alone, of the best constants in Poincar\'e inequality. The key point is the implementation of a refinement of the classical P\'olya-Szeg\"o inequality for the symmetric decreasing rearrangement which yields an optimal weighted Wirtinger inequality.
View Paper: https://www.semanticscholar.org/paper/4d73c1ce6624aac20fcb91f87e877ad09119a914
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Citations in the corpus
- Sharp estimates on the first eigenvalue of the $$p$$p-Laplacian with negative Ricci lower bound (2012, methodology): “It is also worth mentioning that in the Euclidean setting, using a completely different approach based on variational techniques, a sharp estimate on the p-Poincaré constant is obtained in [5], see also [6] for the weighted case.”
- Moduli of continuity, isoperimetric profiles, and multi-point estimates in geometric heat equations (2014, background): “The result for non-negative Ricci curvature was proved previously (for any p > 1) by Valtorta [74], and the special case of convex domains in Euclidean space was proved independently in [43].”