Analysis Seminar

Date: 2021-05-06  16:00-18:00        

Tencent meeting ID：445 587 385

Lecture 1

Title： Stability in Gagliardo-Nirenberg-Sobolev inequalities

Speaker：Nikita Simonov (Universite Paris Dauphine)

Date/Time：2021-05-06 16:00-17:00 pm

Location：Tencent meeting ID：445 587 385

Abstract: In some functional inequalities, best constants and minimizers are known. The next question is stability: suppose that a function "almost attains the equality", in which sense it is close to one of the minimizers? In this talk, a will address a recent result on quantitative stability of a subfamily of Gagliardo-Nirengerg-Sobolev inequalities. The results are based on a joint work with M. Bonforte, J. Dolbeault, and B. Nazaret.

Lecture 2

Title： Sharp estimates for the wave equation via the Penrose transform

Speaker：Giuseppe Negro (University of Birmingham)

Date/Time：2021-05-06 17:00-18:00 pm

Location：Tencent meeting ID：445 587 385

Abstract: In 2004, Foschi found the best constant, and the extremizing functions, for the Strichartz inequality for the wave equation with data in the Sobolev space  $\Hdot^{1/2}\times\Hdot^{-1/2}( R^3 )$, which is also commonly known as the adjoint Fourier restriction estimate to the cone. Foschi formulated a conjecture, concerning the extremizers to this inequality in all spatial dimensions $d\ge 2$. We disprove such conjecture for even $d$, but we provide evidence to support it for odd $d$; in this case the conjecture is true in a local sense. The proofs use the conformal compactification of the Minkowski space-time given by the Penrose transform.

Host：An Zhang

Welcome!