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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)
    to appear in Geom. Funct. Anal.
  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)