T5 configurations and hyperbolic systems

Author:

Johansson Carl Johan Peter1,Tione Riccardo2

Affiliation:

1. École Polytechnique Fédérale de Lausanne, School of Basic Sciences, Station 8, CH-1015, Lausanne, Switzerland

2. Max Planck Institute for Mathematics, in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany

Abstract

In this paper, we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in [B. Kirchheim, S. Müller and V. Šverák, Studying Nonlinear PDE by Geometry in Matrix Space (Springer, 2003), Sec. 7], and many of its properties have already been shown in [A. Lorent and G. Peng, Null Lagrangian measures in subspaces, compensated compactness and conservation laws, Arch. Ration. Mech. Anal. 234(2) (2019) 857–910; A. Lorent and G. Peng, On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity, Calc. Var. Partial Differential Equations 59(5) (2020) 156]. In particular, in [A. Lorent and G. Peng, On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity, Calc. Var. Partial Differential Equations 59(5) (2020) 156], it is shown that the differential inclusion does not contain any [Formula: see text] configurations. Here, we continue that study by showing that the differential inclusion does not contain [Formula: see text] configurations.

Funder

SNSF

Swiss State Secretariat for Education, Research and Innovation

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,General Mathematics

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