Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 23 (2016), No. 2, 347--386Copyright Heldermann Verlag 2016 Thin Elastic Plates Supported over Small Areas. I: Korn's Inequalities and Boundary Layers Giuseppe Buttazzo Dept. of Mathematics, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy buttazzo@dm.unipi.it Giuseppe Cardone Dept. of Engineering, Università del Sannio, Corso Garibaldi 107, 82100 Benevento, Italy giuseppe.cardone@unisannio.it Sergey A. Nazarov Mathematics and Mechanics Faculty, St. Petersburg State University, Universitetsky pr. 28, Stary Peterhof 198504, Russia srgnazarov@yahoo.co.uk [Abstract-pdf] A thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base is considered; the diameter of $\theta_{h}$ is of the same order as the plate relative thickness $h\ll 1$. In addition to the standard Kirchhoff model with the Sobolev point condition, a three-dimensional boundary layer is investigated in the vicinity of the support $\theta_{h}$, which with the help of the derived weighted inequality of Korn's type, will provide an error estimate with the bound $ch^{1/2}|\ln h|$. Ignoring this boundary layer effect reduces the precision order down to $|\ln h|^{-1/2}$. Keywords: Kirchhoff plate, small support zones, asymptotic analysis, boundary layers, weighted Korn inequality. MSC: 74K20, 74B05 [ Fulltext-pdf  (294  KB)] for subscribers only.