Geodesic
Best Constants in Poincaré Inequalities for Convex Domains
Journal of convex analysis, Tome 20 (2013) no. 1, pp. 253-264 Cet article a éte moissonné depuis la source Heldermann Verlag

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We prove a Payne-Weinberger type inequality for the p-Laplacian Neumann eigenvalues (p ≥ 2). The inequality provides the sharp upper bound on convex domains, in terms of the diameter alone, of the best constant in Poincaré inequality. The key point is the implementation of a refinement of the classical Pólya-Szegö inequality for the symmetric decreasing rearrangement which yields an optimal weighted Wirtinger inequality.
Classification : 35B05, 47J05, 26D15
Mots-clés : Poincare inequality, p-Laplacian eigenvalues, Neumann boundary conditions 
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     author = {L. Esposito and C. Nitsch and C. Trombetti},
     title = {Best {Constants} in {Poincar\'e} {Inequalities} for {Convex} {Domains}},
     journal = {Journal of convex analysis},
     pages = {253--264},
     year = {2013},
     volume = {20},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a15/}
}
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L. Esposito; C. Nitsch; C. Trombetti. Best Constants in Poincaré Inequalities for Convex Domains. Journal of convex analysis, Tome 20 (2013) no. 1, pp. 253-264. http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a15/