A proof for the Poincaré inequality with explicit constant for convex domains is given. This proof is a modification of the original proof of L. F. Payne and H. F. Weinberger [Arch. Rat. Mech. Anal. 5 (1960) 286--292], which is valid only for the two-dimensional case.
Cite this article
Mario Bebendorf, A Note on the Poincaré Inequality for Convex Domains. Z. Anal. Anwend. 22 (2003), no. 4, pp. 751–756DOI 10.4171/ZAA/1170