4 citations · 12 across the 21 of their papers we have counts for
25 papers
The Monge-Kantorovich tangent bundle to a measure
Adolfo Arroyo-Rabasa, Averil Aussedat, Guy Bouchitté
We study the tangent bundle to a Radon measure in Euclidean space, introduced by Bouchitté, Champion and Jimenez (2005). Its construction, inspired by Monge-Kantorovich o…
Divergence-free concentrations come from vanishing sequences
Adolfo Arroyo-Rabasa, Francesco Nobili, Ivan Yuri Violo
A vanishing sequence of divergence-free matrix fields is one that is bounded in and is carried by open sets of vanishing volume. Recently established, Bouchitté's…
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…
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--…
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…
Local Poincaré constants and mean oscillation functionals for functions
Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin
We introduce the concept of local Poincaré constant of a function as a tool to understand the relation between its mean oscillation and its total variation at small scales. Th…
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…
A Lebesgue-Lusin property for linear operators of first and second order
Adolfo Arroyo-Rabasa
We prove that for a homogeneous linear partial differential operator of order and an integrable map taking values in the essential range of that operator…
Representation of the total variation as a -limit of -type seminorms
Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin
We address a question raised by Ambrosio, Bourgain, Brezis, and Figalli, proving that the -limit, with respect to the topology, of a family of -type seminor…
New projection and Korn estimates for a class of constant-rank operators on domains
Adolfo Arroyo-Rabasa
Let and let be an open and bounded set of . We establish classical Korn inequalities \[ \inf_{\substack{v \in L^p(Ω)\\\mathcal A v = 0}} \|u - v\|…
An elementary approach to the homological properties of constant-rank operators
Adolfo Arroyo-Rabasa, José Simental
We give a simple and constructive extension of Raiţă's result that every constant-rank operator possesses an exact potential and an exact annihilator. Our construction is completel…
A Bourgain-Brezis-Mironescu representation for functions with bounded deformation
Adolfo Arroyo-Rabasa, Paolo Bonicatto
We establish a non-local integral difference quotient representation for symmetric gradient semi-norms in and , which does not require the manipulation of distributi…
Higher integrability for measures satisfying a PDE constraint
Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch +2
We establish higher integrability estimates for constant-coefficient systems of linear PDEs \[ \mathcal{A} μ= σ, \] where and are ve…
Slicing and fine properties for functions with bounded -variation
Adolfo Arroyo-Rabasa
We study the slicing and fine properties of functions in , the space of functions with bounded -variation. Here, is a homogeneous…
Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge
Adolfo Arroyo-Rabasa, Raphael Winter
We prove that the Debye screening length emerges in a spatially homogeneous plasma described by the nonlinear Vlasov-Poisson equation interacting with a point charge. While screene…
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…
Characterization of generalized Young measures generated by -free measures
Adolfo Arroyo-Rabasa
We give two characterizations, one for the class of generalized Young measures generated by -free measures, and one for the class generated by -gradient mea…
Generalized multi-scale Young measures
Adolfo Arroyo-Rabasa, Johannes Diermeier
This paper is devoted to the construction of generalized multi-scale Young measures, which are the extension of Pedregal's multi-scale Young measures [Trans. Amer. Math. Soc. 358 (…
An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint
Adolfo Arroyo-Rabasa
We give a simple criterion on the set of probability tangent measures of a positive Radon measure , which yields lower bounds on the Hausdorff dimension of $…
Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch +1
We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first…
Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
Adolfo Arroyo-Rabasa, Guido De Philippis, Filip Rindler
We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrar…
Relaxation and optimization for linear-growth convex integral functionals under PDE constraints
Adolfo Arroyo-Rabasa
We give necessary and sufficient conditions for minimality of generalized minimizers for linear-growth functionals of the form \[ \mathcal F[u] := \int_Ωf(x,u(x)) \, \text{d}x, \qq…
Regularity for free interface variational problems in a general class of gradients
Adolfo Arroyo-Rabasa
We present a way to study a wide class of optimal design problems with a perimeter penalization. More precisely, we address existence and regularity properties of saddle points of…