Workshop
| Registration Deadline: | August 01, 2005 almost 18 years ago |
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| To apply for Funding you must register by: | May 15, 2005 about 18 years ago |
| Parent Program: | -- |
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Show List of Speakers
- Patricia Bauman
- Andras Domokos
- Maria del Mar Gonzalez (Polytechnical University of Cataluña (Barcelona) )
- Peng-Fei Guan
- David Hartenstine
- Emmanuel Hebey
- Nikolai Krylov
- Yanyan Li
- Fang-Hua Lin
- Robert McCann (University of Toronto)
- Mikhail Safonov
- Yu Yuan (University of Washington)
This workshop will consists of two main series of lectures, one each day by Luis Caffarelli and Matt Gursky. The intention of these series is to give an overview of the central ideas of the program on Nonlinear Elliptic Equations. In addition there will be several individual lectures on specific topics of current research activitiy. Five lectures by Luis Caffarelli: Basic tools for the regularity theory of nonlinear elliptic equations. How do nonlinear elliptic PDE fit within the calculus of variations? What are fully nonlinear equations, and what do you need to prove regularity? Topics will include: Sobolev embedding versus energy inequalities, geometric arguments, the oscillation theorem of De Giorgi, Calderon--Zygmund type decomposition and the Harnak inequality. Some advanced topics will be the Krylov--Safonov Harnack inequality, and perhaps the Evans--Krylov estimates. Five Lectures by Matt Gursky Some Fully Nonlinear Equations in Geometry The goal of this series of lectures is to describe some examples of fully nonlinear equations which arise in geometry. Although geometrically inspired problems provided the motivation for much of the development of the modern theory of nonlinear PDEs, we will not attempt an historical survey. Rather, we will concentrate on two model problems to illustrate some of the main ideas and techniques: the problem of isometrically embedding a surface in 3D Euclidean space, and the problem of prescribing the sigma-k curvature of a conformal metric. Other invited speakers are: Patricia Bauman , Maria Del Mar Gonzalez, Pengfei Guan, Emmanuel Hebey, Nikolai Krylov, Yan Yan Li, Fang-Hua Lin, Robert McCann, Mikhail Safonov, Yu Yuan. Lecture Schedule Monday August 15 9:30-10:30 Luis Caffarelli:"Basic tools for the regularity theory of nonlinear elliptic equations, I" 10:30-11:00 Tea Break - 2nd Floor 11:00-12:00 Matt Gursky:"Some Fully Nonlinear Equations in Geometry, I" 12:00-1:30 Lunch 1:30-2:30 Patricia E. Bauman: “Nonlinear PDE Methods for Analysis of Phase Transitions in Superconducting and Liquid Crystals” 2:30-3:30 Andras Domokos: “Regularity of quasilinear subelliptic equations” 3:30-4:00 Tea Break - 2nd Floor 4:00-5:00 Yu Yuan: "Resolving the singularities of minimal Hopf cones" Tuesday August 16 9:30-10:30 Luis Caffarelli:"Basic tools for the Regularity Theory of Nonlinear Elliptic Equations, II" 10:30-11:00 Tea Break - 2nd Floor 11:00-12:00 Matt Gursky:"Some Fully Nonlinear Equations in Geometry, II" 12:00-1:30 Lunch 1:30-2:30 Mikhail Safonov: “Boundary behavior of solutions to second order elliptic and parabolic equations in non-smooth domains” 2:30-3:30 Diego Maldonado: “On the regularity of solutions to the Monge-Ampere equation and its linearization” 3:30-4:00 Tea Break - 2nd Floor 4:00-5:00 Nikolai Krylov I: "Numerical approximation for fully nonlinear degenerate equations" Wednesday August 17 9:30-10:30 Luis Caffarelli:"Basic tools for the Regularity Theory of Nonlinear Elliptic Equations, III" 10:30-11:00 Tea Break - 2nd Floor 11:00-12:00 Matt Gursky:"Some Fully Nonlinear Equations in Geometry, III" 12:00-1:30 Lunch 1:30-2:30 Fang-Hua Lin: 2:30-3:30 David A. Hartenstine: 3:30-4:00 Tea Break - 2nd Floor 4:00-5:00 Nikolai Krylov II: "Numerical approximation for fully nonlinear degenerate equations" Thursday August 18 9:30-10:30 Luis Caffarelli:"Basic tools for the Regularity Theory of Nonlinear Elliptic Equations, IV" 10:30-11:00 Tea Break - 2nd Floor 11:00-12:00 Matt Gursky:"Some Fully Nonlinear Equations in Geometry, IV" 12:00-1:30 Lunch 1:30-2:30 Maria Del Mar Gonzalez:: “Construction of singular solutions for a fully non-linear equation in conformal geometry” 2:30-3:30 Emmanuel Hebey: "Fourth order PDEs of critical growth" 3:30-4:00 Tea Break - 2nd Floor 4:00-5:00 Nikolai Krylov III: "Numerical approximation for fully nonlinear degenerate equations" Friday August 19 9:30-10:30 Luis Caffarelli:"Basic tools for the Regularity Theory of Nonlinear Elliptic Equations, V" 10:30-11:00 Tea Break - 2nd Floor 11:00-12:00 Matt Gursky:"Some Fully Nonlinear Equations in Geometry, V" 12:00-1:30 Lunch 1:30-2:30 Yanyan Li: ``Some Liouville type theorems'' 2:30-3:30 Peng-Fei Guan: “A constant rank theorem of convex solutions of fully nonlinear equations” 3:30-4:00 Tea Break - 2nd Floor 4:00-5:00 Robert J. McCann: “Second-order asymptotics for fast nonlinear diffusions”
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Show Funding
To apply for funding, you must register by the funding application deadline displayed above.
Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.
Show Lodging
MSRI does not hire an outside company to make hotel reservations for our workshop participants, or share the names and email addresses of our participants with an outside party. If you are contacted by a business that claims to represent MSRI and offers to book a hotel room for you, it is likely a scam. Please do not accept their services.
MSRI has preferred rates at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Institute discount. To book online visit this page (the MSRI rate will automatically be applied).
MSRI has preferred rates at the Graduate Berkeley, depending on room availability. Reservations may be made by calling 510-845-8981. When making reservations, guests must request the MSRI preferred rate. Enter in the Promo Code MSRI123 (this code is not case sensitive).
MSRI has preferred rates at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select "Affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI." When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).
MSRI has a preferred rates at Easton Hall and Gibbs Hall, depending on room availability. Guests can call the Reservations line at 510-204-0732 and ask for the MSRI- Mathematical Science Research Inst. rate. To book online visit this page, select "Request a Reservation" choose the dates you would like to stay and enter the code MSRI (this code is not case sensitive).
Additional lodging options may be found on our short term housing page.
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Aug 15, 2005 Monday |
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Aug 16, 2005 Tuesday |
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Aug 17, 2005 Wednesday |
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Aug 18, 2005 Thursday |
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Aug 19, 2005 Friday |
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