Volume 26, 2020
|Number of page(s)||11|
|Published online||10 December 2020|
On a question of D. Serre
EPFL SB, Station 8,
2 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.
* Corresponding author: firstname.lastname@example.org
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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