Calculus of Variations and Geometric Measure Theory

C. J. P. Johansson - R. Tione

$T_5$ configurations and hyperbolic systems

created by tione on 20 Dec 2022
modified on 31 Aug 2023

[BibTeX]

Published Paper

Inserted: 20 dec 2022
Last Updated: 31 aug 2023

Journal: Comm. Cont. Math.
Year: 2022
Doi: https://doi.org/10.1142/S021919972250081X

ArXiv: 2208.10979 PDF

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 Section 7 of $[$Kirchheim, Müller, Šverák, 2003$]$ and many of its properties have already been shown in $[$Lorent, Peng, 2019$]$-$[$Lorent, Peng, 2020$]$. In particular, in $[$Lorent, Peng 2020$]$ it is shown that the differential inclusion does not contain any $T_4$ configurations. Here we continue that study by showing that the differential inclusion does not contain $T_5$ configurations.