Higher integrability for measures satisfying a PDE constraint

A Arroyo-Rabasa, G De Philippis, J Hirsch… - Transactions of the …, 2024 - ams.org
We establish higher integrability estimates for constant-coefficient systems of linear
PDEs\[\mathcal {A}\mu=\sigma,\] where $\mu\in\mathcal {M}(\Omega; V) $ and …

Compensation phenomena for concentration effects via nonlinear elliptic estimates

A Guerra, B Raiţă, M Schrecker - arXiv preprint arXiv:2112.10657, 2021 - arxiv.org
We study compensation phenomena for fields satisfying both a pointwise and a linear
differential constraint. This effect takes the form of nonlinear elliptic estimates, where …

Carnot rectifiability and Alberti representations

G Antonelli, EL Donne, A Merlo - arXiv preprint arXiv:2302.01376, 2023 - arxiv.org
This paper introduces and studies the analogue of the notion of Lipschitz differentiability
space by Cheeger, using Carnot groups and Pansu derivatives as models. We call such …