Global structure of the singular set of energy minimising bendings. (30th September 2015)

• Record Type: Journal Article
• Authors: Dall'Acqua, Anna; Hornung, Peter
• Is Part Of: Nonlinearity. Volume 28:Number 11(2015:Nov.)
• Page Start: 3821
• Page End: 3844
• Publication Date: 2015-09-30
• Subjects: nonlinear elasticity -- plate theory -- isometric immersions; 74K20 -- 49Q10 -- 74B20; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/11/3821
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: This article is about deformations minimising Kirchhoff's nonlinear bending energy of plates. An earlier (local) partial regularity result asserts that such deformations are smooth away from a singular set. Here we complement this by providing global results. They allow us to estimate the size of the singular set. More precisely, we study the geometry of planar regions; their boundaries constitute the central part of the singular set. Under natural assumptions on the given boundary data, we show that deformed configurations minimising the bending energy have only finitely many planar regions, and each of them is a polygon. We obtain explicit bounds on the number of such polygons and on the number of edges of each polygon in terms of the boundary data.