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MSRI Summer Microprogram on Nonlinear Partial Differential Equations

July 23, 2007 to August 10, 2007
Organized By: L. C. Evans (UC Berkeley, Chair), C. Gutierrez (Temple), C. Sogge (Johns Hopkins), D. Tataru (UC Berkeley)
 
Participant List:
View a List of Registered Participants
 
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.
 

Schedule

Monday January 1, 2007

08:00AM - 08:00AM  TBD

Monday July 23, 2007

01:00PM - 01:50PM  Panagiotis Souganidis Error estimates for approximations to viscosity solutions of uniformly elliptic second-order pde    (See Abstract)
02:00PM - 02:50PM  Hongjie Dong On the Green's matrices of strongly elliptic and parabolic systems of second order    (See Abstract)
03:00PM - 04:00PM  Afternoon Tea
04:00PM - 04:50PM  Russell Schwab Stationary Ergodic Homogenization of Time Dependent Hamliton-Jacobi    (See Abstract)

Tuesday July 24, 2007

01:00PM - 01:50PM  Young-Heon Kim Curvature and the continuity of optimal transportation maps    (See Abstract)
02:00PM - 02:50PM  Maria Gonzalez Fractional powers of the Laplacian and some applications    (See Abstract)
03:00PM - 04:00PM  Afternoon Tea
04:00PM - 04:50PM  Luigi De Pascale Local solutions and existence of optimal transport maps for the $W_\infty$ Wasserstein distance. Extensions to more classical Monge problems.    (See Abstract)

Wednesday July 25, 2007

01:00PM - 01:50PM  Robert Jensen Super- and sub-solutions of Aronsson equations    (See Abstract)
02:00PM - 02:50PM  Yifeng Yu Asymptotic behaviour of infinity harmonic functions near isolated singularities.    (See Abstract)
03:00PM - 04:00PM  Afternoon Tea
04:00PM - 04:50PM  Sun-Sig Byun Hessian Estimates for fourth order parabolic equations    (See Abstract)

Thursday July 26, 2007

01:00PM - 01:50PM  Cristian Gutierrez The refractor problem in reshaping light beams
02:00PM - 02:50PM  Craig Evans More PDE methods for weak KAM theory
03:00PM - 04:00PM  Afternoon Tea

Monday July 30, 2007

09:00AM - 09:45AM  Christopher Sogge Dispersion, Nonlinear Wave Equations 1
10:00AM - 10:45AM  Cristian Gutierrez The Monge-Ampere Equation 1
11:00AM - 11:45AM  Christopher Sogge Dispersion, Nonlinear Wave Equations 2
12:00PM - 12:45PM  Cristian Gutierrez The Monge-Ampere Equation 2

Tuesday July 31, 2007

09:00AM - 09:50AM  Christopher Sogge Dispersion, Nonlinear Wave Equations 3
10:00AM - 10:30AM  Morning Tea
10:30AM - 11:20AM  Cristian Gutierrez The Monge-Ampere Equation 3
11:40AM - 12:30PM  Christopher Sogge Dispersion, Nonlinear Wave Equations 4

Wednesday August 1, 2007

09:00AM - 09:50AM  Cristian Gutierrez The Monge-Ampere Equation 4
10:00AM - 10:30AM  Morning Tea
10:30AM - 11:20AM  Daniel Tataru Nonlinear Wave Equations 1
11:40AM - 12:30PM  Craig Evans Weak Convergence Methods 1

Thursday August 2, 2007

09:00AM - 09:50AM  Daniel Tataru Nonlinear Wave Equations 2
10:00AM - 10:30AM  Morning Tea
10:30AM - 11:20AM  Craig Evans Weak Convergence Methods 2
11:40AM - 12:30PM  Daniel Tataru Nonlinear Wave Equations 3

Friday August 3, 2007

09:00AM - 09:50AM  Craig Evans Weak Convergence Methods 3
10:00AM - 10:30AM  Morning Tea
10:30AM - 11:20AM  Daniel Tataru Nonlinear Wave Equations 4
11:40AM - 12:30PM  Craig Evans Weak Convergence Methods 4

Monday August 6, 2007

08:30AM - 09:00AM  Coffee and registration
09:00AM - 10:00AM  Michael Christ An a priori bound and weak solvability of the nonlinear Schrodinger equation    (See Abstract)
10:00AM - 11:00AM  Morning break
11:00AM - 12:00PM  Marius Beceanu A Centre-Stable Manifold for the Focussing Cubic NLS in R^{3+1}    (See Abstract)
12:00PM - 02:00PM  Lunch
02:00PM - 03:00PM  Herbert Koch Wellposedness and scattering for KPII
03:00PM - 04:00PM  Afternoon tea
04:00PM - 05:00PM  Slim Ibrahim Around the 2D energy critical NLKG    (See Abstract)

Tuesday August 7, 2007

09:00AM - 10:00AM  Justin Holmer Soliton interaction with delta impurities
10:10AM - 11:00AM  Robert McCann Ricci flow, entropy and mass transport
11:00AM - 12:00PM  Jason Metcalfe Global-in-time Strichartz estimates for asymptotically flat Schr\"odinger equations    (See Abstract)
12:00PM - 02:00PM  Lunch
02:00PM - 03:00PM  Hart Smith Lp bounds on eigenfunctions for Lipschitz metrics    (See Abstract)
03:00PM - 04:00PM  Afternoon tea
04:00PM - 05:00PM  Dan Geba Quadratic nonlinear wave equations    (See Abstract)

Wednesday August 8, 2007

09:00AM - 10:00AM  Jacob Sterbenz Some singular solutions of critical Wave-Maps
10:10AM - 11:00AM  Neil Trudinger On Mass Transport
11:00AM - 12:00PM  Ioan Bejenaru Global solutions for Schroedinger Maps
12:00PM - 05:00PM  Free Afternoon

Thursday August 9, 2007

09:00AM - 10:00AM  Maciej Zworski Local Smoothing in the Presence of Lots of Trapping    (See Abstract)
10:10AM - 11:00AM  Szu-yu Sophie Chen Partial regularity for an elliptic system in geometry
11:00AM - 12:00PM  Becca Thomases Global existence for elastic waves in an exterior domain    (See Abstract)
12:00PM - 02:00AM  Lunch
02:00PM - 03:00PM  Matthew Blair Strichartz estimates on manifolds with boundary    (See Abstract)
03:00PM - 04:00PM  Afternoon tea
04:00PM - 05:00PM  Jeremy Marzuola Stable perturbations of a minimal mass soliton for a saturated nonlinear Schr\"odinger equation in 3D.

Friday August 10, 2007

09:00AM - 10:00AM  Xiangjin Xu Pointwise Carleman estimates and control theoretic implications    (See Abstract)
10:00AM - 11:00AM  Morning Break
11:00AM - 12:00PM  Shijun Zheng TBD

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