Ongoing/In preparation projects

1. Adolfo Arroyo-Rabasa, Stefano Buccheri and Jean Van Schaftingen
   We are developing a characterization of operators satisfying a “Bourgain-Brezis-Mironescu nonlocal representation”

2. Adolfo Arroyo-Rabasa and Guy Bouchitté
   We have proof that the Monge—Kantorovic bundle of a measure coincides with the differentiability bundle defined by Alberti and Marchese. We also introduce the Smirnov bundle of a measure

3. Adolfo Arroyo-Rabasa
   Slicing of linear PDEs by planes. This is a generalization of the work “Slicing and fine properties for functions with bounded A-variation”, which considers the slicing theory for codimension higher than one.

Research Papers

1. Adolfo Arroyo-Rabasa, Paolo Bonicatto and Giacomo Del Nin
   Local Poincaré constants and mean oscillations functionals for BV functions
   2022, 37 pages
   arXiv 2402.10794 (arXiv)

2. Adolfo Arroyo-Rabasa
   A Lebesgue-Lusin property for linear operators of first and second order
   2022, 11 pages
   Proc. Roy. Soc. Edinburgh Sect. A (pdf) (arXiv)

3. Adolfo Arroyo-Rabasa
   Functional and variational aspects of nonlocal operators associated with linear PDEs
   2023, 32 pages
   To appear in Nonlinear Anal. (arXiv)

4. Adolfo Arroyo-Rabasa
   New projection and Korn estimates for a class of constant-rank operators on domains
   2023 (version 2), 41 pages
   arXiv 2109.14602 (arXiv)

5. Adolfo Arroyo-Rabasa and José Simental
   An elementary proof of the homological properties of constant-rank operators
   2023, 24 pages
   C R. Math (pdf)

6. Adolfo Arroyo-Rabasa and Paolo Bonicatto
   A Bourgain–Brezis–Mironescu representation for functions with bounded deformation
   2023, 24 pages
   Calc. Var. and PDEs (pdf) (arXiv)

7. Adolfo Arroyo-Rabasa, Paolo Bonicatto and Giacomo Del Nin
   Representation of the total variation as a Γ-limit of BMO-type seminorms
   2024, 21 pages
   Indiana Univ. Math. J (pdf) (arXiv)

8. Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch, Filip Rindler and Anna Skorobogatova
   Higher integrability for measures satisfying a PDE constraint
   2024, 29 pages
   Trans. Amer. Math. Soc. (arXiv)
   Errata: Concerning the validity of Remark 1.9: The previous to last sentence in p. 6200 should read “In particular, under the assumption that $\mu \le \|T_i\|$ and $\vec{T_i}$ is sufficiently close to $e_i$ at $\|T\|$ almost every point,…”

9. Adolfo Arroyo-Rabasa
   Characterization of generalized Young measures generated by A-free measures
   2021, 90 pages
   Arch. Rat. Mech. Anal (pdf)

10. Adolfo Arroyo-Rabasa and Raphael Winter
    Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge
    2021, 15 pages 
    Comm. Partial Differential Equations (pdf)

11. Adolfo Arroyo-Rabasa, A, Guido De Philippis and Filip Rindler
    Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
    2021, 36 pages
    Adv. Calc. Var. (pdf)

12. Adolfo Arroyo-Rabasa
    Slicing and fine properties for functions with bounded A-variation
    2020, 45 pages
    arXiv 2009.13513 (ArXiv)

13. Adolfo Arroyo-Rabasa
    An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint
    2020, 9 pages
    Proc. Amer. Math. Soc. (pdf)

14. Adolfo Arroyo-Rabasa and Johannes Diermeier
    Generalized multi-scale Young measures
    2020, 48 pages
    SIAM J. Math. Anal. (pdf)

15. Adolfo Arroyo-Rabasa and Anna Skorobogatova
    A look into some of the fine properties of functions with bounded A-variation
    2019, 26 pages
    To appear in ESAIM, Control Optim. Calc. Var. (ArXiv)

16. Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch and Filip Rindler
    Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
    2019, 19 pages
    Geom. Funct. Anal. (pdf)

17. Adolfo Arroyo-Rabasa
    Relaxation and optimization for linear-growth convex integral functionals under PDE constraints
    2017, 39 pages
    J. Funct. Anal. (pdf)

18. Adolfo Arroyo-Rabasa
    Regularity for free interface variational problems in a general class of gradients
    2016, 43 pages
    Calc. Var. Partial Differential Equations (pdf)