Convex integration with linear constraints and its applications

2016/05/08 by Seonghak Kim, Kim, Seonghak
Computer Science · Mathematics · #35D30 #35F60 #Advanced Differential Equations and Dynamical Systems #Advanced Optimization Algorithms Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Matrix Theory and Algorithms #math.AP #msc:35D30 #msc:35F60

paper · pdf · doi:10.48550/arxiv.1605.02340

37 pages

arxiv created 2016/05/08 · openalex publication_date 2016/05/08 · arxiv updated 2016/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study solutions of the first order partial differential inclusions of the form ∇ u∈ K, where u:Ω⊂ℝⁿ→ℝ^m and K is a set of m× n real matrices, and derive a companion version to the result of Müller and Šverák [20], concerning a general linear constraint on the components of ∇ u. We then consider two applications: the vectorial eikonal equation and a T₄-configuration both under linear constraints.

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