Rafayel Teymurazyan
Rafayel Teymurazyan works on nonlinear partial differential equations and free boundary problems arising from applications in bio-technologies, chemical engineering, financial mathematics, and optimal design, among others.
Biography
Rafayel Teymurazyan obtained his PhD in Mathematics from the University of Lisbon (Portugal) in 2013. After postdoc and research positions at the Federal University of Ceará (Brazil), the University of Texas at Austin (USA) and the University of Coimbra (Portugal), he joined KAUST in May of 2023. He works on regularity theory for nonlinear PDEs and the mathematical analysis of free boundary problems.
Research Interests
Rafayel Teymurazyan works on nonlinear partial differential equations (PDEs) and free boundary problems. The term free boundary problem (FBP) refers to a PDE to be solved both for an unknown function and for an unknown domain. FBPs arise in range of mathematical models that are used to describe a physical or biological phenomenon (for example, ice melting into water, population dynamics), or an economical or financial occurrence (American options, stock markets).
About
Recent publications and preprints
- G. Di Fazio, R. Teymurazyan, and J.M. Urbano, Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces, submitted.
- D. dos Prazeres, R. Teymurazyan, and J.M. Urbano, Improved regularity for a nonlocal dead-core problem, arXiv:2504.09557, submitted.
- D.J. Araújo, R. Teymurazyan, and J.M. Urbano, Geometric properties of free boundaries in degenerate quenching problems, arXiv:2402.11536, submitted.
- D. dos Prazeres, A. Sobral, and R. Teymurazyan, The fractional Laplacian uncovered, 35 CBM (2025), to appear.
- R. Teymurazyan, The fractional Laplacian: a primer, Coimbra Mathematical Texts, Springer Cham (2025), to appear.
- D.J. Araújo and R. Teymurazyan, Interacting free boundaries in obstacle problems, Interfaces Free Bound. (2025).
- D.J. Araújo and R. Teymurazyan, Fully nonlinear dead-core systems, J. Funct. Anal. 287 (2024), no. 9, Paper No. 110586, 23pp.
Selected publications
- D.J. Araújo, R. Teymurazyan, and V. Voskanyan, Sharp regularity for singular obstacle problems, Math. Ann. 387 (2023), 1367-1401.
- L.A. Caffarelli, R. Teymurazyan and J.M. Urbano, Fully nonlinear integro-differential equations with deforming kernels, Comm. Partial Differential Equations 45 (2020), 847-871.
- E.V. Teixeira and R. Teymurazyan, Optimal design problems with fractional diffusions, J. Lond. Math. Soc. (2) 92 (2015), 338-352.
Positions held
- 2014 - 2025 researcher, University of Coimbra, Portugal.
- 2016 - 2018 visiting researcher, University of Texas at Austin, TX, USA.
- 2013 - 2014 researcher, Federal University of Ceará, Fortaleza, Brazil.
- 2012 - 2013 researcher, University of Lisbon, Portugal.
Education
- Doctor rerum naturalium (Dr. rer. nat.)
- Mathematics, University of Lisbon, Portugal, 2013