Speaker
Victor Hernandez-Santamaria, Universidad Nacional Autónoma de México
Abstract
In this talk, I will discuss a family of fractional elliptic problems with critical Sobolev exponent, focusing on the role of symmetry. These problems are variational, but the critical exponent creates a lack of compactness, which makes the search for solutions delicate. One way to recover compactness is to restrict the problem to suitable symmetric classes. Depending on the symmetry imposed, this leads to different types of least-energy solutions, including radially symmetric and sign-changing ones. I will also briefly describe a convergence result for these solutions when the order of the fractional operator varies. In particular, when the limiting order is an integer, this gives a way to understand the transition from nonlocal to local critical problems. This is based on joint work with Alberto Saldaña.