A Note on the Poincaré Inequality for Convex Domains

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Poincaré constants for finite element stars (2012, unknown): “1991 Mathematics Subject Classification.”
Theory of adaptive finite element methods: An introduction (2009, unknown): “see [60, 11].”
A remark on optimal weighted Poincar\'e inequalities for convex domains (2012, methodology): “In [23] (see also [2]), it has been proved that, if p 1⁄4 2, and W is convex, in any dimension”
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces (2013, unknown): “If X = [−1, 1] and ρ is uniform, then C1 ≤ 2 √ m/π [3].”
An optimal anisotropic Poincaré inequality for convex domains (2011, unknown): “It should also be interesting to ask if the methods of [Payne and Weinberger 1960] and [Bebendorf 2003] work to reprove our result, since there are lots of motivations in computational mathematics.”
On the Discrete Poincaré–Friedrichs Inequalities for Nonconforming Approximations of the Sobolev Space H 1 (2005, background): “Note however that the constant itself can still be better in the continuous case, see, Payne and Weinberger [10] and Bebendorf [2] for convex domains.”
A Hybrid High-Order method for the incompressible Navier-Stokes equations based on Temam's device (2018, unknown): “[2]), while, for more general element shapes, CP can be estimated in terms of the mesh-regularity parameter %.”