Research Interests

Rafayel Teymurazyan works on free boundary problems and nonlinear PDEs. 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).

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.

Professional Memberships

• 2014 -- 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.