|Speaker||Nguyen Cong Phuc|
|Dept.||Louisiana State Univ.|
Sobolev spaces are spaces of functions whose (weak) derivatives have certain degree of integrability. Associated to each Sobolev space is a Sobolev capacity. Originally appearing in the theory of electrostatics, Sobolev capacities have played an important role in modern analysis as a device to measure smoothness or singularity. In this talk, I will discuss their connection to the so-called trace inequalities and their applications to certain nonlinear elliptic partial differential equations with super-critical non-linearities and measure data. The talk is based on joint work with Igor E. Verbitsky.