Edgard completed his PhD in Mathematics at the Instituto Superior Técnica of the Universidade de Lisboa (Portugal, 2013) under the direction of Diogo Gomes. After the completion of his doctoral work, he held post-doctoral positions at CAMGSD-IST-UL (Lisbon), IMPA (Rio de Janeiro) and ICMC-USP (São Carlos). In November 2016, Prof. Pimentel obtained his Habilitation (Livre-Docência) at USP (ICMC). Since January 2017, Edgard works as Assistant Professor in the Department of Mathematics at Pontifical Catholic University of Rio de Janeiro (PUC-Rio). Researcher of the National Council of Science and Technology (Level 2, CNPq-Brasil) and Jovem Cientista do Estado do Rio de Janeiro (FAPERJ-Brasil), Edgard was recently selected as a Junior Associate Fellow of the International Centre for Theoretical Physics (ICTP-Trieste). In 2019, he was selected as a grantee of the Instituto Serrapilheira.
Prof. Pimentel likes to think about Partial Differential Equations, with emphasis on regularity theory. His research agenda has been developed in close collaboration with researchers based both in Brasil and abroad. Edgard's interaction with the international community is vibrant and includes scientific visits to prestigious and very selected research institutes, such as CIMAT (Guanajuato), Hausdorff Research Institute for Mathematics (Bonn), ICTP (Trieste), Imperial College London, Royal Institute of Technology (Stockholm) and Technion (Israel).
Currently, Prof. Pimentel serves the Brazilian mathematical community, among other instances, as member of evaluation panels for national agencies supporting research in the country.
My research interests are in the Analysis of Partial Differential Equation, with focus on regularity theory. In this context, some of my results examine conditions under which (weak) solutions to some classes of equations present improved regularity. These classes include non-convex elliptic operators as well as degenerate/singular models, both in the linear and the nonlinear settings. Another important question arising in the topic concerns optimal regularity. More recently, I began to think on fractional harmonic maps and (related) free boundary problems.
I have been funded through the usual opportunities (Researcher Fellowship CNPq and Fellowship Jovem Cientista do Estado do Rio de Janeiro FAPERJ) as well as through distinctive, highly selective, funding schemes.
Among the latter I mention the Junior Associate Fellowship (ICTP) and the Public Call 2018 (Instituto Serrapilheira). Among my recent results, I select the following references:
- Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations.
Em co-autoria com A. Bronzi, G. Rampasso and E. Teixeira.
- Improved regularity for the porous medium equation along zero level-sets.
Em co-autoria com M. Santos.
- Geometric regularity for elliptic equations in double-divergence form.
To appear in Analysis and PDE
Em co-autoria com R. Leitão e M. Santos.
- Regularity theory for the Isaacs equation through approximation methods.
Ann. Inst. H. Poincaré Anal. Non Linéaire (2019) 36.
- Regularity theory for second-order stationary mean-field games.
Indiana Univ. Math. J. (2017) 66.
Em co-autoria com V. Voskanyan.
- Sharp Hessian integrability for nonlinear elliptic equations: an asymptotic approach.
J. Math. Pures Appl. (2016) 106.
Em co-autoria com E. Teixeira.