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.
Mots-clés : Matrix-fields, determinants, integrability
@article{COCV_2020__26_1_A97_0, author = {De Rosa, Luigi and Tione, Riccardo}, title = {On a question of {D.} {Serre}}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {26}, year = {2020}, doi = {10.1051/cocv/2020021}, mrnumber = {4185067}, zbl = {1460.26010}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2020021/} }
TY - JOUR AU - De Rosa, Luigi AU - Tione, Riccardo TI - On a question of D. Serre JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2020021/ DO - 10.1051/cocv/2020021 LA - en ID - COCV_2020__26_1_A97_0 ER -
De Rosa, Luigi; Tione, Riccardo. On a question of D. Serre. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 97. doi : 10.1051/cocv/2020021. http://archive.numdam.org/articles/10.1051/cocv/2020021/
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