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Mathematics Institute

Dr Adolfo Arroyo-Rabasa

  Profile

Adolfo Arroyo-Rabasa

Research Fellow
 
Office: B2.15
Phone: +44 (0)24 761 50903
Email: adolfo dot arroyo-rabasa at warwick dot ac dot uk


I did my Ph.D. under the supervision of S. Müller at the University of Bonn. Currently I am a Research Fellow in the University of Warwick as part of the research group SINGULARITY from Filip Rindler.

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
  • Rigidty properties of PDE constrained structures
  • Regularity theory of elliptic PDE's and stochastic elliptic PDE's
  • Convex Analysis methods for variational problems

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

NOTE: Soon I will start a reading group about on the paper 'High-dimensionality and h-principle' (PDE Bulletin AMS 2017) by L. Székelyhidi & C. De Lellis. If you are interested to join please get in contact by e-mail.

Publications

  1. Generalized multi-scale Young measures (joint work with J. Diermeier)
    arXiv:1901.04755
  2. An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint
    arXiv: 1812.07629
  3. Dimensional estimates and rectifiability for measures satisfying linear PDE constraints (joint work with G. De Philippis, J. Hirsch, and F. Rindler) arXiv:1811.01847
  4. Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints (joint work with G. De Philippis and F. Rindler)
    to appear in Adv. Calc. Var.
  5. Relaxation and optimization for linear-growth convex integral functionals under PDE constraints
    J. of Funct. Anal. 273 (2017)
  6. Regularity for free interface variational problems in a general class of gradients
    Calc. Var. PDE's 55 (2016)

Current projects

  • Characterization of tangent functions of bounded deformation and its applications in the calculus of variations