Program

The research in nonlinear elliptic equations is one of the most developed in Mathematics, and of great importance because of its interaction with other areas within Mathematics and for its applications in broader scientific disciplines such as fluid dynamics, phase transitions, mathematical finance and image processing in computer science. The past few decades have witnessed many new developments in this area including the understanding of fully nonlinear equations, singularities and symmetric properties of solutions. These advances yield a better understanding of global geometry, Yamabe problem, De Giorgi conjecture and the equations for superconductors. However, there are still many interesting questions to be resolved. This semester program at MSRI will concentrate in this area with the purpose of bringing together people working on different aspects of the various problems, to appraise the current status of development, to encourage interactions between these different points of view, and to assess future directions.