| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 97 | |
| Number of page(s) | 11 | |
| DOI | https://doi.org/10.1051/cocv/2020021 | |
| Published online | 10 December 2020 | |
On a question of D. Serre
1
EPFL SB, Station 8,
CH-1015
Lausanne, Switzerland.
2
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190,
CH-8057
Zurich, Switzerland.
* Corresponding author: riccardo.tione@math.uzh.ch
Received:
17
October
2019
Accepted:
16
April
2020
In this paper we give a negative answer to the question posed in D. Serre (Ann. Inst. Henri Poincaré C Anal. Non linéaire 35 (2018) 1209–1234, Open Question 2.1) about possible gains of integrability of determinants of divergence-free, non-negative definite matrix-fields. We also analyze the case in which the matrix-field is given by the Hessian of a convex function.
Mathematics Subject Classification: 26B25 / 39B42 / 39B62 / 49N60
Key words: Matrix-fields / determinants / integrability
© EDP Sciences, SMAI 2020
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