Dr Adolfo Arroyo-Rabasa
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Adolfo Arroyo-RabasaResearch Fellow |
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
- Generalized multi-scale Young measures (joint work with J. Diermeier)
arXiv:1901.04755
- An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint
arXiv: 1812.07629 - 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. - 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. - Relaxation and optimization for linear-growth convex integral functionals under PDE constraints
J. of Funct. Anal. 273 (2017) - Regularity for free interface variational problems in a general class of gradients
Calc. Var. PDE's 55 (2016)