Convex integration with linear constraints and its applications

Seonghak Kim

doi:10.1016/j.jmaa.2020.124028

Convex integration with linear constraints and its applications

Seonghak Kim

Research output: Contribution to journal › Article › peer-review

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 [16], 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.

Original language	English
Article number	124028
Journal	Journal of Mathematical Analysis and Applications
Volume	487
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2020.124028
State	Published - 15 Jul 2020

Keywords

Baire's category method
Convex integration
Linear constraints
Partial differential inclusions
T-configuration
Vectorial eikonal equation

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10.1016/j.jmaa.2020.124028

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abstract = "We study solutions of the first order partial differential inclusions of the form ∇u∈K, where u:Ω⊂Rn→Rm and K is a set of m×n real matrices, and derive a companion version to the result of M{\"u}ller and {\v S}ver{\'a}k [16], 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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AB - We study solutions of the first order partial differential inclusions of the form ∇u∈K, where u:Ω⊂Rn→Rm and K is a set of m×n real matrices, and derive a companion version to the result of Müller and Šverák [16], 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.

KW - Baire's category method

KW - Convex integration

KW - Linear constraints

KW - Partial differential inclusions

KW - T-configuration

KW - Vectorial eikonal equation

UR - https://www.scopus.com/pages/publications/85081230047

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DO - 10.1016/j.jmaa.2020.124028

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

Convex integration with linear constraints and its applications

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Keywords

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