## On the upper semicontinuity of a quasiconcave functional

created by tione on 28 Nov 2020

[BibTeX]

Published Paper

Inserted: 28 nov 2020
Last Updated: 28 nov 2020

Journal: Journal of Functional Analysis
Volume: 279
Year: 2020
Doi: https://doi.org/10.1016/j.jfa.2020.108660

ArXiv: 1906.06510 PDF

Abstract:

In the recent paper \cite{SER}, the second author proved a divergence-quasiconcavity inequality for the following functional $\mathbb{D}(A)=\int_{\mathbb{T}^n} det(A(x))^{\frac{1}{n-1}}\,dx$ defined on the space of $p$-summable positive definite matrices with zero divergence. We prove that this implies the weak upper semicontinuity of the functional $\mathbb{D}(\cdot)$ if and only if $p>\frac{n}{n-1}$.