Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 4, 2003, pp. 751–756
DOI: 10.4171/ZAA/1170

A Note on the Poincaré Inequality for Convex Domains

Mario Bebendorf[1]

(1) Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10/11, 04109, LEIPZIG, GERMANY

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.

Keywords: Poincaré inequality, convex domains

Bebendorf M. A Note on the Poincaré Inequality for Convex Domains. Z. Anal. Anwend. 22 (2003), 751-756. doi: 10.4171/ZAA/1170