Research Papers

Geometric Measure Theory (Currents in Metric Spaces and PDE constrained measures)

• Adolfo Arroyo-Rabasa and Guy Bouchitté
  Structural properties of one-dimensional metric currents: SBV-representations, connectedness and the flat chain conjecture
  2025, 52 pages
  arXiv 2508.08212 (arXiv)

• 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)

• 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)

• 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)

Fine properties in functions under PDE constraints (complex elliptic and elliptic operators)

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

• 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)

Calculus of variations: Lower semicontinuity, quasiconvexity and Young measures

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

• 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)

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

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

Non-local energies and non-local operators associated with PDEs

• Adolfo Arroyo-Rabasa, Paolo Bonicatto, and Giacomo Del Nin
  Local Poincaré constants and mean oscillations functionals for BV functions
  2024, 37 pages
  arXiv 2402.10794 (arXiv)

• 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)

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

• 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)

Functional Inequalities in the context of PDEs

• 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)

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

• 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,…”

Mathematical Physics

• 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)

Partial regularity of free boundary problems

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