International Workshop on Elliptic and Kinetic Partial Differential Equations

Thematic Program on Current Trends in Analysis and Partial Differential Equations

IMPA, Rio de Janeiro, July, 6 – 17

Escolas de Altos Estudos

IMPA, Rio de Janeiro, 06 de julho a 06 de agosto de 2015

Este curso será ministrado pelo Prof. Luis A. Caffarelli, da University of Texas at Austin – USA,  no âmbito da Escola de Altos Estudos da Capes.

As aulas serão ministradas no IMPA e transmitidas para todo o Brasil pela internet e disponibilizadas no endereço: http://video.impa.br/index.php?page=altos-estudos-free-boundary-problems

Apresentação

Curso: Free Boundary Problems: Common Aspects and Methods

IMPA, Rio de Janeiro, 06 de julho a 06 de agosto de 2015

Apresentação

Luis A. Caffarelli is a world leading expert in the field of nonlinear partial differential equations and free boundary problems. Since 1996 he holds the Sid Richardson Chair in Mathematics at the University of Texas at Austin. He also has been a professor at the University of Minnesota, the University of Chicago, the Institute for Advanced Study and the Courant Institute of Mathematical Sciences at New York University.

He received the Bôcher Prize in 1984. He also received the prestigious Rolf Schock Prize in Mathematics of the Royal Swedish Academy of Sciences, the Leroy P. Steele Prize for Lifetime Achievement in Mathematics, the Solomon Lefschetz medal, and the Wolf Prize in Mathematics. In 2014, he was also awarded the Leroy P. Steele Prize for Seminal Contribution to Research by the AMS. In 1991, he was elected to the National Academy of Sciences.

The focus of Professor Caffarelli’s research has been in the area of elliptic nonlinear partial differential equations and their applications. Caffarelli received great recognition with his breakthrough paper “The regularity of free boundaries in higher dimensions” published in 1977 in Acta Mathematica. He developed several regularity results for fully nonlinear elliptic equations including the Monge-Ampere equation. He is also famous for his contributions to homogenization. Recently, he has taken an interest in Integro-differential equations.

This current proposal fosters the visit of Professor Luis Caffarelli to the Instituto Nacional de Matemática Pura e Aplicada – IMPA, to deliver the course entitled OBSTACLE TYPE FREE BOUNDARY PROBLEMS, which will also be part of the Thematic Program Current Trends in Analysis and Partial Differential Equations, to be held at IMPA from July 01 to September 30th, 2015. The ideal scientific atmosphere nourished by the Thematic program shall enhance even further the benefits of the course to the mathematical Brazilian community.

The course will bring together graduate students, pos-docs as well as researchers to witness one of the most beautiful chapters of the modern theory of PDEs presented by its primary star. The research in partial differential equations is well represented in Brazil, and there will certainly be a very good receptivity of this course in the calendar year of 2015.

Calendário

1a semana (06 a 09/07), segunda, terça, quarta e quinta-feira das 16:30 às 18:00h – Auditório Ricardo Mañé

2a semana (13 a 16/07), segunda, terça, quarta e quinta-feira das 16:30 às 18:00h – Auditório Ricardo Mañé

3a semana (20 e 21/07), segunda e terça-feira das 16:30 às 18:00h – Auditório 3

4a semana (27 a 31/07), Nesta semana não haverá aula devido ao 300 Colóquio Brasileiro de Matemática

5a semana (03 a 04/08), segunda e terça-feira das 16:30 às 18:00h – Auditório 3

 

Cartaz

 

Inscrição

Todas as aulas serão transmitidas pela internet. Os Programas de Pós-Graduação são convidados a participar, incluindo este curso como parte das suas atividades acadêmicas e atribuindo-lhe créditos. Também será possível assistir ao curso presencialmente no IMPA.

Para inscrição é necessário o envio da seguinte documentação:

Formulário de inscrição preenchido.
– Histórico escolar atualizado (graduação, mestrado e doutorado).

 

 

OBS.: Todos participantes deverão realizar o cadastro de dados pessoais no sistema online do Ensino.

Para mais informações:
Divisão de Ensino
Estrada Dona Castorina 110,  Jardim Botânico
Rio de Janeiro, RJ, CEP 22460-320, Brazil
E-mail: ensino@impa.br
Tel: (55 21) 2529-5011(55 21) 2529-5011 / 5016 / 5024
Fax:(55 21) 2529-5015

Programa

Abstract :
We will discuss several mathematical problems exhibiting the formation of free boundaries, and develop some tools and structures to approach them.

Content:
1: Some basic tools: Properties of solutions to diffusion processes: second oreder equations in divergence and non divergence forms, variational and Perrons (viscosity methods) for second order equations. Interior and boundary Harnack inequalities for second order divergence equations.

2. a) The obstacle problem: optimal regularity and non degeneracy, blow up methods, free boundary regularity, similarities with the thery of boundary regularity for sets of minimal perimeter (minimal surfaces) b) Cavitation type problems: non-variational approach, minimal solutions, optimal regularity and non-degeneracy, a “Harnack inequality” approach: Lipschitz free boundaries are smooth.

c) The Signorini problem (a non-local obstacle problem): Description of the problem, basic properties of the solution, regularity properties, some monotonicity properties, free boundary regularity.

3: Recapitulate, informal discussion of topics and problems.

 

Vídeos das aulas

Accommodation

The Organizing Committee is reserving hotel for the invited lecturers.

Rio de Janeiro has a large number of hotels. Lately, for the main congresses, we have been using Hotel Acapulco, Everest Rio Hotel, Everest Park Hotel, Hotel Debret, Hotel Vermont, among others. To take advantage of IMPA´s special rate, please contact Ms. Michele Leite at MMX Eventos – micheleleite@mmxcongressos.com – phone: 55 21 2210-1732 55 21 2210-1732 or visit their homepage at: http://www.mmxcongressos.com/?lang=en

We also indicate a very good cost/benefit hotel in Copacabana: Residencial Apart Hotel – http://www.apartt.com.br/english/index.htm
Please contact the Hotel directly.

For other type of accommodation like hostels and bed and breakfast, we suggest the following:

Bed&Breakfast (very close to IMPA and strongly recommended)
Pouso Verde
Rua Caminhoá, 14 – Jardim Botânico
Tel: 55 21 2529-2942 55 21 2529-2942 , 55 21 99971-0511
e-mail:pousoverde@globo.com http://pousoverde.org/

Hostels

Lagoa:
Rioow Hostel
Rua Saturnino de Brito – 190 on the corner of av. Borges de Medeiros – Lagoa
Tel: 55 21 3988-3004, 55 21 3988-4008
E-mail: contato@rioow.com
http://www.rioowhostel.com.br/en/

Botafogo:

Jabanga Hostel
Rua Paulo Barreto, 123 – Botafogo
Tel: 55(21) 3597-030455(21) 3597-0304
http://www.jabangahostel.com/

Meiai Hostel:
R. Guilhermina Guinle, 127 – Botafogo Tel: 55(21) 3495-448155(21) 3495-4481
http://www.meiai.com.br/

Copacabana:

Pousada Girassol
Travessa Angrense, 25 A – Copacabana (entre Santa Clara e Raimundo Correa)
Tel: 55(21)2256-695155(21)2256-6951 / Fax: 55(21) 2286-5652
www.girassolpousada.com.br/
pousada@girassolpousada.com.br

Humaitá:

Lagoa Guest House
Rua do Humaitá, 392 – Humaitá
Tel: 55(21) 3518-900055(21) 3518-9000
E-mail: contato@lagoaguesthouse.com
www.lagoaguesthouse.com/

Ipanema:

Che Lagarto Ipanema
Rua Paul Redfern 48 – Ipanema
Tel: 55(21) 2512-807655(21) 2512-8076
www.chelagarto.com

Leblon:
Leblon Spot (associado à Hostelling International)
Rua Dias Ferreira, 626 – Leblon
Tel: 55(21) 2137-009055(21) 2137-0090
E-mail: contact@leblonspot.com
www.leblonspot.com

Please check availability and prices directly with them

Committees

Organizing Committee

Ricardo Alonso (PUC – Rio)
Emanuel Carneiro (IMPA)
Diego Moreira (UFC)
Boyan Sirakov (PUC – Rio)
Eduardo Teixeira (UFC)

Scientific Committee

Ricardo Alonso (PUC – Rio)
Luis Caffarelli (Texas – Austin)
Emanuel Carneiro (IMPA)
Lawrence C. Evans (Berkeley)
Irene M. Gamba (Texas – Austin)
Diego Moreira (UFC)
Boyan Sirakov (PUC – Rio)
Eduardo Teixeira (UFC)

Certificates

Speaker

Mini-course

Participation

Poster Presentation

Picture of the Group

Picture

Program

1st Week – School (July 6-10, 2015)

Schedule

2nd Week – Conference (July 13-17, 2015)

Schedule

Poster Session

The acalmar Chern-Simons equation
Adilson Eduardo Presoto (Universidade Federal de São Carlos – UFSCAR)

Elliptic equations in thin domains with oscillatory boundary
Ariadne Nogueira (Instituto de Matemática e Estatística IME – USP)

Estimativas a Priori para Problemas Elípticos via Desigualdade de Hardy-Sobolev
Jose Miguel Mendoza Aranda (Universidade Federal de São Carlos – UFSCAR)

Periodic solutions for a 1D-model with nonlocal velocity field via mass transport
Julio Cesar Valencia Guevara (IMECC – UNICAMP)

PDEs in Neuronal Dynamics and Brain Disorders
Pedro Doria Maia (University of Washington – UW)

Instructions for Poster Presentation

Due to the size of the poster boards your poster may not exceed 90 cm in width and 120 cm in height (portrait format). Materials for mounting the posters will be available at the poster areas.

Local organizers will provide the necessary materials for the setup, but please remember that there will be no possibility to print out the posters at the conference site.

The title and Author(s) Name(s) must appear on the top of the final poster. The poster should have a balance between the text and illustrations. The illustrations should have a bigger area of the poster. Font size should be large enough to enable reading from a certain distance. It is suggested the following font size:

Title: Size 70 (1,5cm H)
Author(s) Name(s): Size 50 (1cm H)
Text: Size 28 (0,7cm H)

Poster Submission

Participants, specially students, are encouraged to submit posters. For that, everybody must be registered in the School/Conference in order to submit it.

The poster proposal should include:

1. name of author
2. institution
3. title
4. Abstract (2 or 3 pages)

The text must be processed directly from LaTex to the .PDF format. The .PDF and .tex files should be sent to the e-mail eventos@impa.br no later than July 17, 2015

Contributed Talks

Friday – July 10th

Nome: Dennis Kriventsov (University of Texas at Austin – USA)
Título: Free boundary problem related to thermal insulation
Hora: 14:00 – 14:20

Nome: Robin Neumayer (University of Texas at Austin – USA)
Título: A strong form of the quantitative Wulff inequality
Hora: 14:20 – 14:40

Nome: Juliana F.S. Pimentel (ICMC – USP – Brazil)
Título: Asymptotic behavior of nondissipative scalar reaction-diffusion equations
Hora: 14:40 – 15:00

Nome: Javier Morales (University of Texas at Austin – USA)
Título: Self propelled particles, Optimal transportation and the logarithmic Sobolev inequality
Hora: 15:00 – 15:20

Nome: Roberto Velho (KAUST – Saudi Arabia)
Título: A Short Introduction to Mean Field Games
Hora: 15:20 – 15:40

Nome: David Evangelista da Silveira Junior (KAUST – Saudi Arabia)
Título: Generalised mean-field games with congestion
Hora: 15:40 – 16:00

COFFEE BREAK: 16:00 – 16:30

Nome: Yash Jhaveri (University of Texas at Austin – USA)
Título: Nonlinear Behavior of the Monge-Ampère Equation in Holder Spaces
Hora: 16:30 – 16:50

Nome: Léonard Monsaingeon (University of Texas at Austin – IST-Lisbon)
Título: A new optimal transport distance between nonnegative measures in R^d
Hora: 16:50 – 17:10

Nome: Maja Taskovic (University of Texas at Austin – USA)
Título: Exponential tails for solutions to the homogeneous Boltzmann equation
Hora: 17:10 – 17:30

Nome: Edgard Pimentel (UFC & UFSCAR – Brazil)
Título: Elliptic Mean Field Games Systems
Hora: 17:30 – 17:50

Nome: Juan Spedaletti (Universidad de San Luis – CONICET Argentina)
Título: Convergence Results for the Steklov eigenvalue and optimal windows in Oscillating Domains
Hora: 17:50 – 18:10

Nome: Rohit Jain (University of Texas at Austin – USA)
Título: The Fully Nonlinear Stochastic Impulse Control Problem
Hora: 18:10 – 18:30

Registration and Financial Support – Deadline for requesting financial support: April 30th, 2015 Answer by June 5th, 2015

Prices for Registration

Category Prices
Professors (Ph.D´s) R$ 150,00
Students (Master and Ph.D) R$ 70,00
IMPA’s Students R$ 40,00

Sponsors

Speakers

Escola de Altos Estudos:

Luis Caffarelli (Texas – Austin)
Free Boundary Problems: Common aspects and methods.

Minicursos:

Luigi Ambrosio (Scuola Normale Superiore – Pisa)
Flow of nonsmooth vector fields and applications. Part I.

Henri Berestycki (CNRS/EHESS – Paris)
Reaction-diffusion and propagation in non-homogenous media

Alessio Figalli (Texas – Austin)
Flow of nonsmooth vector fields and applications. Part II.

Irene Gamba (Texas – Austin)
Analytical issues for non-local multi-linear interaction models: The Boltzmann and related equations

Lecture Presentation

Arshak Petrosyan (Purdue)
The Thin Obstacle Problem.

Laure Saint-Raymond (École Normale Supérieure – Paris)
From particle systems to collisional kinetic equations.

Yannick Sire (Aix-Marseille)
KAM for PDES.

Lihe Wang (Iowa)
Regularity theory of elliptic equations

Visas

Participants should check, as soon as possible (in view of the time it may take to obtain a visa), whether a visa is needed for Brazil. Visas are not required for Latin American and EU citizens. They are, however, required for all citizens of countries which request visas from Brazilian citizens. Please visit http://impa.br/opencms/en/eventos/informacao/informacoes_visto.htmlfor more information.