This is a weekely event organized by the UConn SIAM Students Chapter.

Brezis-Nirenberg problem considers semilinear elliptic equations whose nonlinearity is associated with the critical Sobolev exponent. In this talk we will discuss the recent progress of the higher order Brezis-Nirenberg problem on hyperbolic spaces. Our results include the existence and nonexistence of solutions, the symmetry of solutions and the solution gap phenomenon. These results are deeply related to the sharp Hardy-Sobolev-Maz’ya inequalities with higher order derivatives and Helgason-Fourier analysis theory. This is a joint work with Guozhen Lu and Qiaohua Yang.