02 September - 13 December 2013
The theory of non-linear evolutionary partial differential equations (PDEs) is of fundamental importance in mathematical analysis and through recent breakthroughs and insights it has reached a stage where some difficult and important questions can be fruitfully addressed. This program will focus on a large class of singular and degenerate PDEs ranging from flows by mean curvature to the infinity Laplacian. Although these equations have a common structure, they are connected to many different applications such as the diffusion in highly non-homogeneous media. A crucial role in understanding non-linear phenomena is played by regularity estimates based only on the structure of the equations. In several ways the recent advances open up a whole new area of research similar to the progress that started a few decades ago concerning regularity and free boundary problems for linear PDEs. The new methods have already turned out to be powerful enough to solve previously unreachable problems.
University of Oxford
NTNU - Norwegian University of Science and Technology
University of Parma