Integral Estimates for Approximations by Volume Preserving Maps

2017/04/18 by Christopher Policastro, Policastro, Christopher
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1704.05198

openalex publication_date 2017/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A quantitative Brenier decomposition shows that the deviation of a map from volume preserving is bounded by the deviation of the derivative from volume preserving. A study of the matrix nearness problem for SL(n) and Sp(2n) relates the estimate to incompressible deformations of elastic materials.

Citations

• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity
• Polar factorization and monotone rearrangement of vector‐valued functions

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