6 papers
Quantified rigidity of -free Young measure concentrations
Adolfo Arroyo-Rabasa, Averil Aussedat
We establish quantitative stability of the De Philippis--Rindler rigidity on conical convex regions. By constructing -quasiconvex functions with a tailored concavity--…
Complex-ellipticity, dimensional estimates and plane wave rigidity in
Adolfo Arroyo-Rabasa
We characterize complex-elliptic operators through a hierarchy of overdeterminacy (-vanishing) quantifying the structural twisting of their symbols. This frame…
Affine rigidity of functions with additive oscillation
Adolfo Arroyo-Rabasa, Sergio Conti
We prove that a locally integrable function must be affine if its mean oscillation, considered as a function of intervals, can be extended to a locally fini…
Structural properties of one-dimensional metric currents: SBV-representations, connectedness and the flat chain conjecture
Adolfo Arroyo-Rabasa, Guy Bouchitté
A comprehensive study of one-dimensional metric currents and their relationship to the geometry of metric spaces is presented. We resolve the one-dimensional flat chain conjecture…
A look into some of the fine properties of functions with bounded -variation
Adolfo Arroyo-Rabasa, Anna Skorobogatova
We establish certain fine properties for functions of bounded -variation known in the classical setting. Here, is a th order constant-coefficient h…
Functional and variational aspects of nonlocal operators associated with linear PDEs
Adolfo Arroyo-Rabasa
We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and s…