On a question of D. Serre
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 97

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.

DOI : 10.1051/cocv/2020021
Classification : 26B25, 39B42, 39B62, 49N60
Keywords: Matrix-fields, determinants, integrability 
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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

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