# Mini-courses and Conference on Nonlinear Elliptic Equations

Hill Center

Organized by Yanyan Li (Rutgers University) and Fanghua Lin (Courant Institute). These activities are financed by NSF-DMS-FRG: Collaborative Research : Emerging Issues in the Sciences Involving Non-Standard Diffusion, coordinated by Henri Berestycki, Luis Caffarelli, Yanyan Li, Fanghua Lin and Luis Silvestre.

During May 13-22, 2013, we will have a concentration period involving issues on nonlinear elliptic and parabolic equations with non-standard diffusion and applications.

The first part, May 13-18, will be at Rutgers University, while the second part, May 20-22, will be at Courant Institute.

Poster for detailed information.

### Activities

$$\blacktriangleright$$ Part I. May 13-18, 2013, Rutgers University

Mini-course by Luis Caffarelli
The Monge–Ampère equation and some nonlocal variations

Mini-course by C. Robin Graham
Dirichlet problem on asymptotically hyperbolic manifolds

Mini-course by Fanghua Lin
A couple of problems in the theory of homogenization

Mini-course by Juncheng Wei
Gluing methods and entire solutions of nonlinear field equations pdf

Special lectures:

Xavier Cabré
Sharp isoperimetric inequalities via the ABP method

Marí­a del Mar González
The CR fractional Laplacian and the fractional CR Yamabe problem

Tianling Jin
Solutions of some Monge–Ampère equations with degeneracy or singularities

Eduardo Teixeira
Free boundary problems and their geometric regularity theory

Michael Vogelius
Approximate cloaking by mapping

Changyou Wang
Global weak solution of the general Ericksen-Leslie system in dimension two

Lei Zhang
Blowup solutions to Liouville systems and Toda systems

First two days (May 13, 14): CoRE Building Lecture Hall

May 15-18: Hill Center 705

$$\blacktriangleright$$ Part II. May 20-22, 2013, Courant Institute

Recent Advances in Nonlinear Partial Differential Equations

$$*$$ to be confirmed.

### Getting Involved

If you are interested in participating, please fill the registration form.

Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).