International Workshop on Elliptic and Kinetic Partial Differential Equations 2015
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.
Apresentação
Curso: Free Boundary Problems: Common Aspects and Methods
IMPA, Rio de Janeiro, 06 de julho a 06 de agosto de 2015
Apresentação
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
Inscrição
Para inscrição é necessário o envio da seguinte documentação:
– Formulário de inscrição preenchido.
– Histórico escolar atualizado (graduação, mestrado e doutorado).
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.
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
Picture of the Group
Program
1st Week – School (July 6-10, 2015)
2nd Week – Conference (July 13-17, 2015)
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
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
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)
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
Postal Address: Instituto Nacional de Matemática Pura e Aplicada
Estrada Dona Castorina 110, Jardim Botânico
Rio de Janeiro, RJ, CEP 22460-320, Brasil
E-mail: eventos@impa.br
