报告人：Dorin Bucur
题目: Degenerate free discontinuity problems and spectral inequalities in quantitative form
时间：2021年7月8日（星期四）下午4:00-5:00
地点：Zoom link：https://zoom.us/j/95945565853?pwd=TFI2RzFsQi9BQVhTSlR4VWdpMFZEZz09
zoom会议号 : 959 4556 5853
密码 : R2DS2V
邀请人：李沁峰
Abstract: We introduce a new geometric-analytic functional that we analyse in the context of
free discontinuity problems.This is motivated by searching quantitative inequalities for best
constants of Sobolev-Poincaré inequalities with trace terms in $R^n$ which correspond to fundamental
eigenvalues associated to semilinear problems for the Laplace operator with Robin boundary conditions.
Our method is based on the study of this new, degenerate, functional which involves an obstacle
problem in interaction with the jump set. Ultimately, this becomes a mixed free discontinuity/free
boundary problem occuring above/at the level of the obstacle, respectively.
This talk is based on joint work with A. Giacomini, M. Nahon.
报告人简介：Dorin Bucur，是偏微分方程、几何变分和椭圆算子谱理论领域著名的学者，在Acta Math、JEMS、
JDG、Adv Math、Anal.PDE、ARMA、JMPA、TAMS、JDE、JFA、SIAM J. Math. Anal.、Proc. Lond. Math. Soc.
等高水平杂志发表一百余篇文章。
