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Home » MSRI Summer Microprogram on Nonlinear Partial Differential Equations

Workshop

MSRI Summer Microprogram on Nonlinear Partial Differential Equations July 23, 2007 - August 10, 2007
Registration Deadline: July 09, 2007 over 7 years ago
To apply for Funding you must register by: April 23, 2007 over 7 years ago
Organizers L. C. Evans (UC Berkeley, Chair), C. Gutierrez (Temple), C. Sogge (Johns Hopkins), D. Tataru (UC Berkeley)
Speaker(s) No Speakers Assigned Yet.
Description

This three week program will emphasize the overlapping research areas of nonlinear dispersive equations (NDE) and nonlinear elliptic equations (NEE), and is intended as an extension of the MSRI programs in these fields from Fall, 2005, with a focus on subsequent research developments. Weeks 1 and 3 will comprise informal but focused workshops on NEE and NDE, respectively. Topics of emphasis will include regularity estimates for elliptic PDE, with applications to mass transport problems and to image processing. The NDE workshop will focus upon eigenfunction estimates, resonances and spectral resolutions for elliptic operators on manifolds. Week 2 will be devoted to several expository minicourses, of general interest, especially for younger mathematicians. We are currently planning these lecture series:

  • Craig Evans, "Survey of weak convergence methods for nonlinear PDE'"
  • Cristian Gutierrez, "The Monge-Ampere equation''
  • Chris Sogge, "Dispersion and existence theorems for nonlinear wave equations"
  • Daniel Tataru, "Nonlinear wave equations''

A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: TQ0000. The cut-off date for reservations is Jun 22, 2007.


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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.

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MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code 123MSRI. Our preferred rate is $139 per night for a Deluxe Queen/King, based on availability.

MSRI has preferred rates of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

MSRI has preferred rates of $110 - $140 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 “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

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Schedule
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Jul 23, 2007
Monday
01:00 PM - 01:50 PM
  Error estimates for approximations to viscosity solutions of uniformly elliptic second-order pde
Panagiotis Souganidis (University of Texas)
02:00 PM - 02:50 PM
  On the Green's matrices of strongly elliptic and parabolic systems of second order
Hongjie Dong
04:00 PM - 04:50 PM
  Stationary Ergodic Homogenization of Time Dependent Hamliton-Jacobi
Russell Schwab
Jul 24, 2007
Tuesday
01:00 PM - 01:50 PM
  Curvature and the continuity of optimal transportation maps
Young-Heon Kim (University of British Columbia)
02:00 PM - 02:50 PM
  Fractional powers of the Laplacian and some applications
Maria Gonzalez
04:00 PM - 04:50 PM
  Local solutions and existence of optimal transport maps for the $$W_\infty$$ Wasserstein distance. Extensions to more classical Monge problems.
Luigi De Pascale
Jul 25, 2007
Wednesday
01:00 PM - 01:50 PM
  Super- and sub-solutions of Aronsson equations
Robert Jensen (Loyola University)
02:00 PM - 02:50 PM
  Asymptotic behaviour of infinity harmonic functions near isolated singularities.
Yifeng Yu
04:00 PM - 04:50 PM
  Hessian Estimates for fourth order parabolic equations
Sun-Sig Byun
Jul 26, 2007
Thursday
01:00 PM - 01:50 PM
  The refractor problem in reshaping light beams
Cristian Gutierrez
02:00 PM - 02:50 PM
  More PDE methods for weak KAM theory
Lawrence Evans (University of California, Berkeley)
Jul 30, 2007
Monday
09:00 AM - 09:45 AM
  Dispersion, Nonlinear Wave Equations 1
Christopher Sogge (Johns Hopkins University)
10:00 AM - 10:45 AM
  The Monge-Ampere Equation 1
Cristian Gutierrez
11:00 AM - 11:45 AM
  Dispersion, Nonlinear Wave Equations 2
Christopher Sogge (Johns Hopkins University)
12:00 PM - 12:45 PM
  The Monge-Ampere Equation 2
Cristian Gutierrez
Jul 31, 2007
Tuesday
09:00 AM - 09:50 AM
  Dispersion, Nonlinear Wave Equations 3
Christopher Sogge (Johns Hopkins University)
10:30 AM - 11:20 AM
  The Monge-Ampere Equation 3
Cristian Gutierrez
11:40 AM - 12:30 PM
  Dispersion, Nonlinear Wave Equations 4
Christopher Sogge (Johns Hopkins University)
Aug 01, 2007
Wednesday
09:00 AM - 09:50 AM
  The Monge-Ampere Equation 4
Cristian Gutierrez
10:30 AM - 11:20 AM
  Nonlinear Wave Equations 1
Daniel Tataru (University of California, Berkeley)
11:40 AM - 12:30 PM
  Weak Convergence Methods 1
Lawrence Evans (University of California, Berkeley)
Aug 02, 2007
Thursday
09:00 AM - 09:50 AM
  Nonlinear Wave Equations 2
Daniel Tataru (University of California, Berkeley)
10:30 AM - 11:20 AM
  Weak Convergence Methods 2
Lawrence Evans (University of California, Berkeley)
11:40 AM - 12:30 PM
  Nonlinear Wave Equations 3
Daniel Tataru (University of California, Berkeley)
Aug 03, 2007
Friday
09:00 AM - 09:50 AM
  Weak Convergence Methods 3
Lawrence Evans (University of California, Berkeley)
10:30 AM - 11:20 AM
  Nonlinear Wave Equations 4
Daniel Tataru (University of California, Berkeley)
11:40 AM - 12:30 PM
  Weak Convergence Methods 4
Lawrence Evans (University of California, Berkeley)
Aug 06, 2007
Monday
09:00 AM - 10:00 AM
  Christ-1
Michael Christ (University of California, Berkeley)
02:00 PM - 03:00 PM
  Koch-1
Herbert Koch (Rheinische Friedrich-Wilhelms-Universität Bonn)
04:00 PM - 05:00 PM
  Around the 2D Energy of NLKG
Slim Ibrahim (University of Victoria)
Aug 07, 2007
Tuesday
09:00 AM - 10:00 AM
  Holmer-1
Justin Holmer
11:00 AM - 12:00 PM
  McCann-1
Robert McCann (University of Toronto)
11:00 AM - 12:00 PM
  Global-in-time Strichartz estimates for asymptotically flat Schr\"odinger equations
Jason Metcalfe
02:00 PM - 03:00 PM
  Lp Bounds on Eigenfunctions for Lipschitz Metrics
Hart Smith (University of Washington)
04:00 PM - 05:00 PM
  Quadratic Linear Wave Equations
Dan Geba
Aug 08, 2007
Wednesday
09:00 AM - 10:00 AM
  Sterbenz-1
Jacob Sterbenz
10:00 AM - 11:00 AM
  Tradinger-1
Neil Trudinger (Australian National University)
11:00 AM - 12:00 PM
  Global solutions for Schroedinger Maps
Ioan Bejenaru
Aug 09, 2007
Thursday
09:00 AM - 10:00 AM
  Local Smoothing in the Presence of Lots of Trapping
Maciej Zworski (University of California, Berkeley)
10:00 AM - 11:00 AM
  S. Chen-1
Szu-yu Sophie Chen
11:00 AM - 12:00 PM
  Thomases-1
Becca Thomases
02:00 PM - 03:00 PM
  Strichartz Estimates on Manifolds with Boundary
Matthew Blair
04:00 PM - 05:00 PM
  Marzuola-1
Jeremy Marzuola
Aug 10, 2007
Friday
09:00 AM - 10:00 AM
  Xu-1
Xiangjin Xu