Adolfo Arroyo-Rabasa Research Fellow   Office: B1.26 Phone: +44 (0)24 761 50903 Email: adolfo dot arroyo-rabasa at warwick dot ac dot uk

I obtained my Ph.D. in October 2017 under the supervision of S. Müller at the University of Bonn. Currently, I am a Research Fellow as part of the research group SINGULARITY led by Filip Rindler.

Teaching Responsibilities 2019/20:
Term 2: MA3G1 Theory of PDEs

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Areas of specialization

• Calculus of Variations
• Geometric Measure Theory
• Regularity theory of Minimal Surfaces and their generalizations
• Classical and stochastic homogenization theory

Research interests

During my short career I have developed a great interest for these topics:

• Lower semicontinuity of integral functionals and quasiconvexity
• Rigidity and fine properties of PDE constrained structures
• Regularity theory of elliptic PDE's
• Convex Analysis and Harmonic Analysis methods for variational problems

I am also very interested in learning optimal transport, convex integration techniques, and Riemannian geometry.

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Publications

1. A Bourgain-Brezis-Mironescu representation for functions of bounded deformation (with P. Bonicatto)
   arXiv:2106.06954
2. Higher integrability for measures satisfying a PDE constraint (with G. De Philippis, J. Hirsch, F. Rindler and A. Skorobogatova)
   arXiv:2106.03077
3. Slicing and fine properties of functions with bounded $\mathcal{A}$-variation
   arXiv:2009.13513
4. Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge (with R. Winter)
   Comm. Partial Differential Equations (2021)
5. On the fine properties of elliptic operators (with A. Skorobogatova)
   arXiv:1911.08474
6. Characterization of generalized Young measures generated by $\mathcal{A}$-free measures
   to appear in Arch. Ration. Mech. Anal. (arXiv:1908.03186)
7. Generalized multi-scale Young measures (joint work with J. Diermeier)
   SIAM J. Math. Anal. 52(4) (2020)
8. An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint
   Proc. Amer. Math. Soc. 148(1) (2020)
9. Dimensional estimates and rectifiability for measures satisfying linear PDE constraints (joint work with G. De Philippis, J. Hirsch, and F. Rindler)
   Geom. Funct. Anal. 29(3) (2019)
10. Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints (joint work with G. De Philippis and F. Rindler)
    Adv. Calc. Var. 13(3) (2020)
11. Relaxation and optimization for linear-growth convex integral functionals under PDE constraints
    J. of Funct. Anal. 273 (2017)
12. Regularity for free interface variational problems in a general class of gradients
    Calc. Var. PDE's 55 (2016)

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