Analysis and Probability seminar

Abstract: A classical result in the theory of Sobolev spaces states that for a bounded domain, the L^q-norm of a function vanishing on the boundary can be controlled by the L^p-norm of its gradient whenever q ≤ p*. Interestingly, the equality case of this inequality has not been thoroughly understood when the exponent q lies strictly between p and p*. I will discuss uniqueness properties of extremals for this inequality. In particular, I will present some results for q close to p and for the case q = ∞. The talk is based on joint work with Lorenzo Brasco and Ryan Hynd.