Edgard A. Pimentel
Centre for Mathematics @ University of Coimbra

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 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.

Publications

Papers submitted to scientific journals
1

BMO-regularity for a degenerate transmission problem
w/ Vincenzo Bianca and José Miguel Urbano
PDF on arXiv

2

Flipping regularity via the Harnack approach and applications to nonlinear elliptic problems
w/ Diego Moreira
PDF on arXiv

3

A Hessian-dependent functional with free boundaries and applications to mean-field games
w/ Julio Correa
PDF on arXiv

4

A fully nonlinear degenerate free transmission problem
w/ Gerardo Huaroto, Giane Rampasso and Andrzej Święch
PDF on arXiv

Papers published in scientific journals
1

A fully nonlinear free transmission problem
To appear in Interfaces Free Bound.
w/ Makson Santos
PDF on arXiv

2

Potential estimates for fully nonlinear elliptic equations with bounded ingredients
Math. Eng. (2023) 5
w/ Miguel Walker
PDF from the journal

3

Fully nonlinear Hamilton-Jacobi equation of degenerate type
Nonlinear Anal. (2023) 227
w/ David Jesus and José Miguel Urbano
PDF from the journal

4

A note on the density of the partial regularity result in the class of viscosity solutions
Rev. Un. Mat. Argentina (2022) 63
w/ Disson dos Prazeres and Giane Rampasso
PDF from the journal (Open access)

5

C1-regularity for degenerate diffusion equations
Adv. Math. (2022) 409
w/ Pêdra Andrade, Daniel Pellegrino and Eduardo Teixeira
PDF from the journal

6

Fractional Sobolev regularity for fully nonlinear elliptic equations
Comm. Partial Differential Equations (2022) 47
w/ Makson Santos and Eduardo Teixeira
PDF from the journal

7

Existence of solutions to a fully nonlinear free transmission problem
J. Differ. Equ. (2022) 320
w/ Andrzej Święch
PDF from the journal (Open access)

8

Stationary fully nonlinear mean-field games
J. Anal. Math. (2021) 145
w/ Pêdra Andrade
PDF from the journal

9

Improved regularity for the porous medium equation along zero level-sets
Israel J. Math. (2021) 245
w/ Makson Santos
PDF from the journal

10

Existence and improved regularity for a nonlinear system with collapsing ellipticity
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) (2021) 22
w/ José Miguel Urbano
PDF from the journal

11

Non-convex Hamilton-Jacobi equations with gradient constraints
Nonlinear Anal. (2021) 210
w/ Héctor Chang-Lara
PDF from the journal

12

On some singular mean-field games
J. Dyn. Games (2021) 8
w/ Marco Cirant, Diogo Gomes and Héctor Sánchez-Morgado
PDF from the journal

13

Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations
J. Funct. Anal. (2020) 279
w/ Anne Bronzi, Giane Rampasso and Eduardo Teixeira
PDF from the journal

14

On a mean field optimal control problem
Nonlinear Anal. (2020) 199
w/ José Carrillo and Vardan Voskanyan
PDF from the journal

15

Geometric regularity for elliptic equations in double-divergence form
Anal. PDE (2020) 13
w/ Raimundo Leitão and Makson Santos
PDF from the journal

16

Improved regularity for the p-Poisson equation
Nonlinearity (2020) 33
w/ Giane Rampasso and Makson Santos
PDF from the journal

17

Regularity theory for the Isaacs equation through approximation methods
Ann. Inst. H. Poincaré Anal. Non Linéaire (2019) 36
PDF from the journal

18

Interior Sobolev regularity for fully nonlinear parabolic equations
Calc. Var. PDE. (2017) 56
w/ Ricardo Castillo
PDF from the journal

19

Regularity theory for second-order stationary mean-field games
Indiana Univ. Math. J. (2017) 66
w/ Vardan Voskanyan
PDF from the journal

20

Sharp Hessian integrability for nonlinear elliptic equations: an asymptotic approach
J. Math. Pures Appl. (2016) 106
w/ Eduardo Teixeira
PDF from the journal

21

Time dependent mean-field games in the superquadratic case
ESAIM Control Optim. Calc. Var. (2016) 22
w/ Diogo Gomes and Héctor Sánchez-Morgado
PDF from the journal

22

Estimates for a class of slowly non-dissipative reaction-diffusion equations
Rocky Mountain J. Math. (2016) 46
w/ Juliana Pimentel
PDF from the journal

23

Time dependent mean-field games with logarithmic nonlinearities
SIAM J. Math. Anal. (2015) 47
w/ Diogo Gomes
PDF from the journal

24

Time dependent mean-field games in the subquadratic case
Comm. Partial Differential Equations (2015) 40
w/ Diogo Gomes and Héctor Sánchez-Morgado
PDF from the journal

Book chapters
1

Asymptotic methods in regularity theory for nonlinear elliptic equations: a survey
Pierre Cardaliaguet et al. (Eds.) PDE Models for Multi-Agent Phenomenon, Springer-Verlag (2018)
w/ Makson Santos

2

Regularity for mean-field games systems with initial-initial boundary conditions: the subquadratic case
Jean-Pierre Bourguignon et al. (Eds.) Dynamics, Games and Sciences III, Springer-Verlag (2015)
w/ Diogo Gomes

Books published
1

Elliptic regularity theory by approximation methods.
London Mathematical Society Lecture Notes Series, Cambridge University Press 2022

2

Regularity theory for mean-field game systems.
SpringerBriefs in Mathematics, Springer-Verlag 2016
w/ Diogo Gomes and Vardan Voskanyan

3

Economic models and mean-field games theory.
IMPA Mathematical Publications - 30th Braz. Math. Colloquium 2015
w/ Diogo Gomes and Levon Nurbekyan

Research

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.

Agenda

My scientific visits

  • Oct

    2023

    Madrid

    2023 Thematic Period PDEs ICMAT-UAM
    Euro-Japanese Conference on Nonlinear Diffusions
    Invited speaker

  • 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

Vincenzo Bianca, since 2021
Thesis: TBA
Co-advisor: Prof. José Miguel Urbano
Department of Mathematics, U. Coimbra

2

Claudemir Alcantara, since 2021
Thesis: TBA
Department of Mathematics, PUC-Rio

3

Miguel Walker, since 2019
Thesis: Regularity theory for fractional harmonic maps (tentative)
Co-advisor: Prof. Yannick Sire
Department of Mathematics, PUC-Rio

4

David Jesus, Since 2018
Thesis: Sharp regularity for degenerate fully nonlinear equations
Co-advisor: Prof. José Miguel Urbano
Department of Mathematics, U. Coimbra

Former graduate students
1

Edison Cuba, Jul 2021
Existence and regularity of solutions for nonlocal and nonlinear models
Department of Mathematics, PUC-Rio
Placement: Post-doctoral fellow, IMECC-Unicamp (funded by FAPESP)

2

Makson Sales Santos, Aug 2020
Regularity theory for fully nonlinear models: interfaces and free boundaries
Department of Mathematics, PUC-Rio
Placement: Research scientist, CAMGSD Instituto Superior Técnico

3

Pêdra Daricléa Santos Andrade, Aug 2020
Towards a regularity theory for fully nonlinear models
Department of Mathematics, PUC-Rio
Placement: Research scientist, CAMGSD Instituto Superior Técnico

4

Giane Casari Rampasso, Feb 2019
On the regularity theory for a class of state-dependent degenerate diffusions
Department of Mathematics, Unicamp
Placement: Assistant Professor, Universidade Federal de Itajubá, UNIFEI

Contact

Department of Mathematics - University of Coimbra

3001 – 501 Coimbra, Portugal
edgard.pimentel [at] mat [dot] uc [dot] pt