Edgard completed his PhD in Mathematics at the Instituto Superior Técnico 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). Jovem Cientista do Estado do Rio de Janeiro (FAPERJ-Brasil), Edgard is a Junior Associate Fellow of the International Centre for Theoretical Physics (ICTP-Trieste). He was a Grantee of the Instituto Serrapilheira (2019-2021) and a Researcher of the National Council for Science and Technology (CNPq-Brazil, 2018-2021). In December 2019, Prof. Pimentel was ellected an Affiliated Member of the Brazilian Academy of Sciences. Working as a Research Scientist at the Centre for Mathematics at the University of Coimbra, Edgard is Assistant Professor at PUC-Rio (on leave).
Prof. Pimentel likes to think about Partial Differential Equations, with emphasis on regularity theory and free boundary problems involving fully nonlinear problems. Recently, Edgard has grown fond of harmonic maps and their variations. His agenda has included visits to important research centers, such as CIMAT (Guanajuato), Hausdorff Research Institute for Mathematics (Bonn), ICTP (Trieste), Imperial College London, Institute of Mathematics of the Polish Academy of Sciences (IMPAN, Warsaw), Max Planck Institute for Mathematics in the Sciences (Leipzig), Mittag-Leffler Institute (Sweden), Royal Institute of Technology (Stockholm), and Technion (Israel). An enthusiast of scientific outreach, has contributed to the blog Ciência Fundamental, produced by Instituto Serrapilheira and Folha de São Paulo.
To download my complete CV, click here.
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BMO-regularity for a degenerate transmission problem
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Flipping regularity via the Harnack approach and applications to nonlinear elliptic problems
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A Hessian-dependent functional with free boundaries and applications to mean-field games
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A fully nonlinear degenerate free transmission problem
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A fully nonlinear free transmission problem
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Potential estimates for fully nonlinear elliptic equations with bounded ingredients
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Fully nonlinear Hamilton-Jacobi equation of degenerate type
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A note on the density of the partial regularity result in the class of viscosity solutions
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C1-regularity for degenerate diffusion equations
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Fractional Sobolev regularity for fully nonlinear elliptic equations
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Existence of solutions to a fully nonlinear free transmission problem
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Stationary fully nonlinear mean-field games
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Improved regularity for the porous medium equation along zero level-sets
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Existence and improved regularity for a nonlinear system with collapsing ellipticity
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Non-convex Hamilton-Jacobi equations with gradient constraints
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On some singular mean-field games
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Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations
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On a mean field optimal control problem
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Geometric regularity for elliptic equations in double-divergence form
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Improved regularity for the p-Poisson equation
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Regularity theory for the Isaacs equation through approximation methods
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Interior Sobolev regularity for fully nonlinear parabolic equations
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Regularity theory for second-order stationary mean-field games
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Sharp Hessian integrability for nonlinear elliptic equations: an asymptotic approach
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Time dependent mean-field games in the superquadratic case
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Estimates for a class of slowly non-dissipative reaction-diffusion equations
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Time dependent mean-field games with logarithmic nonlinearities
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Time dependent mean-field games in the subquadratic case
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Asymptotic methods in regularity theory for nonlinear elliptic equations: a survey
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Regularity for mean-field games systems with initial-initial boundary conditions: the subquadratic case
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Elliptic regularity theory by approximation methods.
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Regularity theory for mean-field game systems.
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Economic models and mean-field games theory.
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My research interests sit at the intersection of Regularity Theory for (nonlinear) Partial Differential Equations (PDE), Free Boundary Problems and Geometric Analysis.
Learning Seminar on Analysis of PDEs: click here for information
Click here for my profile on GoogleScholar
Click here for my profile on Mathematical Reviews
Click here to watch a lecture of mine at the Hausdorff Research Institute (Bonn)
Click here to watch a lecture of mine at BIRS-Banff
Note: if you are a graduate student or a young post-doc interested in working in my group, please do not hesitate in dropping me a line.
Oct
2023
2023 Thematic Period PDEs ICMAT-UAM
Euro-Japanese Conference on Nonlinear Diffusions
Invited speaker
Feb
2023
Scientific visit to
Cristiana de Filippis and
Giuseppe Mingione
Jan
2023
Lisbon WADE
Invited speaker
Dec
2022
Projeto Delfos
Invited speaker (scientific outreach)
Nov
2022
Mittag-Leffler Institute
Research program
Geometric Aspects of Nonlinear PDEs
Oct
2022
IV Congresso de Jovens Pesquisadores em Matemática
Pleanry speaker
Sep
2022
Nonuniformly elliptic problems
Invited speaker
Aug
2022
Encontro Conjunto Brasil-Portugal
Plenary speaker
Jul
2022
International Congress of Mathematicians
ICM2022 (Remote)
Jul
2022
Three Nonlinear Days in Coimbra: a CAMGSD-CMUC Workshop in Nonlinear Analysis
Co-organized w/ Hugo Tavares
May-Jul
2022
Scientific Visit
ICTP
Mar
2022
SIAM Conference on Analysis of PDE
Mar
2022
Scientific visit to Pêdra Andrade, Makson Santos and Hugo Tavares
Instituto Superior Técnico
Jan
2022
CMUC Analysis Seminar
Oct
2021
An introduction to mean-field games
Shanghai Jiao Tong U.
Invited by Prof. Kaizhi Wang
Sep
2021
TWAS-TYAN Virtual workshop on PDE
Sep
2021
Free boundary problems 2021
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Vincenzo Bianca, since 2021
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Claudemir Alcantara, since 2021
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Miguel Walker, since 2019
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David Jesus, Since 2018
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Edison Cuba, Jul 2021
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Makson Sales Santos, Aug 2020
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Pêdra Daricléa Santos Andrade, Aug 2020
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Giane Casari Rampasso, Feb 2019
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3001 – 501 Coimbra, Portugal
edgard.pimentel [at] mat [dot] uc [dot] pt