The Monge-Ampère constraint: Matching of isometries, density and regularity, and elastic theories of shallow shells

详细信息    查看全文

• 作者：Marta Lewicka^a ; ^{lewicka@pitt.edu} ; L. Mahadevan^b ; ^{lm@seas.harvard.edu} ; Mohammad Reza Pakzad^a ; ^{pakzad@pitt.edu}
• 关键词：35B65 ; 53C24 ; 74K25 ; 74B20
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2017
• 出版时间：January-February 2017
• 年：2017
• 卷：34
• 期：1
• 页码：45-67
• 全文大小：458 K
• 卷排序：34

文摘

The main analytical ingredients of the first part of this paper are two independent results: a theorem on approximation of W2,2W2,2 solutions of the Monge–Ampère equation by smooth solutions, and a theorem on the matching (in other words, continuation) of second order isometries to exact isometric embeddings of 2d surface in R3R3.In the second part, we rigorously derive the Γ-limit of 3-dimensional nonlinear elastic energy of a shallow shell of thickness h  , where the depth of the shell scales like hαhα and the applied forces scale like hα+2hα+2, in the limit when h→0h→0. We offer a full analysis of the problem in the parameter range α∈(1/2,1)α∈(1/2,1). We also complete the analysis in some specific cases for the full range α∈(0,1)α∈(0,1), applying the results of the first part of the paper.