Short Bio
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 2016, Prof. Pimentel obtained his Habilitation (Livre-Docência) at USP (ICMC). Pimentel was selected as a Jovem Cientista do Estado do Rio de Janeiro (2018) and is a former grantee of Instituto Serrapilheira. A Junior Associate Fellow of the International Centre for Theoretical Physics (ICTP, Trieste), Prof. Edgard was ellected an Affiliate Member of the Brazilian Academy of Sciences (ABC) in 2019. In 2024, Edgard was selected to join the Seminário de Jovens Cientistas of the Lisbon Academy of Sciences. With previous professorial positions in São Paulo and Rio de Janeiro, Edgard is currently an Associate Professor with Habilitation (Agregação) in the Department of Mathematics at the University of Coimbra and a researcher at the Centre for Mathematics at the same University (CMUC).
Prof. Pimentel likes to think about Partial Differential Equations, with emphasis on regularity theory and free boundary problems involving fully nonlinear models. Recently, Edgard has grown fond of harmonic maps and their variations. An enthusiast of scientific outreach, has contributed to the blog Ciência Fundamental, produced by Instituto Serrapilheira and Folha de São Paulo.
Publications
Papers submitted to scientific journals
| 1 |
Numerical methods for fully nonlinear degenerate diffusions
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2 |
Regularity of Convex envelopes (A geometric approach)
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3 |
Fully nonlinear free boundary problems: optimal boundary regularity beyond convexity
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4 |
Boundary regularity for a fully nonlinear free transmission problem
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5 |
On super-solutions to fully nonlinear equations with measurable ingredients
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|---|
Papers published in scientific journals
| 1 |
Differentiability of solutions for a degenerate fully nonlinear free transmission problem
|
2 |
Hessian regularity in Hölder spaces for a semi-linear bi-Laplacian equation
|
3 |
Improved regularity for Hessian-dependent functionals
|
4 |
A fully nonlinear degenerate free transmission problem
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5 |
A Hessian-dependent functional with free boundaries and applications to mean-field games
|
6 |
BMO-regularity for a degenerate transmission problem
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7 |
A fully nonlinear free transmission problem
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| 8 |
Potential estimates for fully nonlinear elliptic equations with bounded ingredients
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| 9 |
Fully nonlinear Hamilton-Jacobi equation of degenerate type
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| 10 |
A note on the density of the partial regularity result in the class of viscosity solutions
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| 11 |
C1-regularity for degenerate diffusion equations
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| 12 |
Fractional Sobolev regularity for fully nonlinear elliptic equations
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| 13 |
Existence of solutions to a fully nonlinear free transmission problem
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| 14 |
Stationary fully nonlinear mean-field games
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| 15 |
Improved regularity for the porous medium equation along zero level-sets
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| 16 |
Existence and improved regularity for a nonlinear system with collapsing ellipticity
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| 17 |
Non-convex Hamilton-Jacobi equations with gradient constraints
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| 18 |
On some singular mean-field games
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| 19 |
Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations
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| 20 |
On a mean field optimal control problem
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| 21 |
Geometric regularity for elliptic equations in double-divergence form
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| 22 |
Improved regularity for the p-Poisson equation
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| 23 |
Regularity theory for the Isaacs equation through approximation methods
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| 24 |
Interior Sobolev regularity for fully nonlinear parabolic equations
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| 25 |
Regularity theory for second-order stationary mean-field games
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| 26 |
Sharp Hessian integrability for nonlinear elliptic equations: an asymptotic approach
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| 27 |
Time dependent mean-field games in the superquadratic case
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| 28 |
Time dependent mean-field games with logarithmic nonlinearities
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| 29 |
Time dependent mean-field games in the subquadratic case
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Book chapters
| 1 |
Asymptotic methods in regularity theory for nonlinear elliptic equations: a survey
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| 2 |
Regularity for mean-field games systems with initial-initial boundary conditions: the subquadratic case
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Books published
| 1 |
Elliptic regularity theory by approximation methods.
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| 2 |
Regularity theory for mean-field game systems.
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| 3 |
Economic models and mean-field games theory.
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Editorial activity
| 1 |
Modern Methods in the Analysis of Free Boundary Problems
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| 2 |
Differential and Algorithmic Intelligent Game Theory
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Research
My research interests sit at the intersection of Regularity Theory for (nonlinear) Partial Differential Equations (PDE), Free Boundary Problems and Geometric Analysis.
2025 Seminar on the Obstacle Problem: 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.
Agenda
My scientific visits
-
Jul
2026
Athens
The 15th AIMS Conference
Invited Speaker
Special session 'Regularity in local versus nonlocal problems' -
Aug
2025
São Paulo
9th IST-IME
Invited Speaker -
Aug
2025
Rio de Janeiro
Carlos Tomei Fest
Invited Speaker -
Jul
2025
Lisbon
Encontro Ciência 2025
Invited Speaker
Round table entitled
Cruzando duas culturas: ciências exatas e humanindades -
Jul
2025
Guimarães
Nonlinear PDE in Guimarães
Plenary Speaker -
Jul
2025
Coimbra
Summer JIM Days
Invited Speaker
Round table on science communication -
Jun/Jul
2025
Coimbra
Scientific visit
Prof. Ryan Hynd (UPenn)
Supported by CMUC -
Jun
2025
Coimbra
Scientific visit
Prof. Nicolau Saldanha (PUC-Rio)
Supported by CMUC -
Jun
2025
Glasgow (cancelled)
The 30th Biennial Numerical Analysis Conference
Contributed talk -
Jun
2024
Coimbra
Scientific visit
Prof. Felix Del Teso (Madrid)
Supported by CMUC -
May
2025
Coimbra
Scientific visit
Prof. Mikko Parviainen (Helsinki)
Supported by CMUC -
Feb
2024
Aveiro
Seminar - Functional Analysis and Applications Group
Invited Speaker -
Feb
2025
Online/GaTech
Virtual Analysis and PDE Seminar
Invited Speaker -
Nov
2024
Coimbra
Scientific visit
Prof. Julio Cesar Correa (UERJ, Brazil)
Supported by CMUC -
Nov
2024
São Carlos
UFSCar Workshop on PDEs 2024 edition
70th birthday of Olimpio H. Miyagaki
Invited Speaker -
Nov
2024
Coimbra
Scientific visit
Prof. Damião Araújo (UFPB, Brazil) -
Oct
2024
Lyon
Scientific visit to Prof. Filippo Santambrogio
Institut Camille Jordan
Université Claude Bernard - Lyon 1
Campus France -
Jul
2024
Coimbra
Regularity theory and free boundary problems: from PDE to Interfaces
Satellite Conference ECM2024
Chair of the OC -
Jul
2024
Seville
European Congress of Mathematics 2024 ECM2024
Co-organizer of a Mini-Symposium -
May
2024
Plovdiv
Modern Methods in Nonlinear Elliptic and Parabolic PDE
Invited Speaker -
Nov
2023
Oxford
Scientific visit to José Carrillo
OxPDE Lunchtime Seminar Series
Oxford -
Oct
2023
Madrid
2023 Thematic Period PDEs ICMAT-UAM
Euro-Japanese Conference on Nonlinear Diffusions
Invited Speaker -
May
2023
Guanajuato
Scientific visit to Héctor Chang-Lara
CIMAT, Guanajato -
Apr-May
2023
London
Agenda blocked
-
Apr
2023
Coimbra
Meeting w/ the Evaluation Committee of
UC|UP PhD Program in Mathematics -
Apr
2023
Milan
Analysis seminar and
scientific visit to Marta Calanchi -
Mar
2023
Prague
Public colloquium
Charles University, Prague -
Feb
2023
Parma
Scientific visit to
Cristiana de Filippis and
Giuseppe Mingione -
Jan
2023
Lisbon
Lisbon WADE
Invited speaker -
Dec
2022
Coimbra
Projeto Delfos
Invited speaker (scientific outreach) -
Nov
2022
Sweden
Mittag-Leffler Institute
Research program
Geometric Aspects of Nonlinear PDEs -
Oct
2022
João Pessoa, Brazil
IV Congresso de Jovens Pesquisadores em Matemática
Pleanry speaker -
Sep
2022
Warsaw
Nonuniformly elliptic problems
Invited speaker -
Aug
2022
Salvador, Bahia
Encontro Conjunto Brasil-Portugal
Plenary speaker -
Jul
2022
Planet Earth
International Congress of Mathematicians
ICM2022 (Remote) -
Jul
2022
Coimbra
Three Nonlinear Days in Coimbra: a CAMGSD-CMUC Workshop in Nonlinear Analysis
Co-organized w/ Hugo Tavares -
May-Jul
2022
Trieste
Scientific Visit
ICTP -
Mar
2022
Berlin
SIAM Conference on Analysis of PDE
-
Mar
2022
Lisbon
Scientific visit to Pêdra Andrade, Makson Santos and Hugo Tavares
Instituto Superior Técnico -
Jan
2022
Coimbra
CMUC Analysis Seminar
-
Oct
2021
Shanghai (remote)
An introduction to mean-field games
Shanghai Jiao Tong U.
Invited by Prof. Kaizhi Wang -
Sep
2021
Trieste (remote)
TWAS-TYAN Virtual workshop on PDE
-
Sep
2021
Berlin (remote)
Free boundary problems 2021
Supervision and teaching
Current graduate students
| 1 |
Ortenilton dos Santos Filho, since 2023
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Former graduate students
| 1 |
Vincenzo Bianca, Sep 2024
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|---|---|
| 2 |
Miguel Walker, Dec 2023
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| 3 |
David Jesus, Apr 2023
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| 4 |
Edison Cuba, Jul 2021
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| 5 |
Makson Sales Santos, Aug 2020
|
| 6 |
Pêdra Daricléa Santos Andrade, Aug 2020
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| 7 |
Giane Casari Rampasso, Feb 2019
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Contact
Department of Mathematics - University of Coimbra
3000 – 143 Coimbra, Portugal