数学物理及偏微分方程国际系列论坛（13）：Nonlinear diffusions, entropy methods and stability

发布时间：2024-12-02 作者：浏览次数：

Speaker:	Professor Jean Dolbeault	DateTime:	Beijing time: 16: 00--17: 00 pm, Dec. 3rd (Tuesday), 2024
Brief Introduction to Speaker: Jean Dolbeault现为法国巴黎九大数学教授，主要从事非线性偏微分方程、数学物理、变分理论等领域的理论研究，特别是在泛函不等式等领域做出过具有国际影响力的系列研究成果，在Invent. Math.、PNAS、JEMS等国际顶尖数学期刊上发表论文180余篇。		Place:	Zoom Meeting ID: 886 6719 5622, Passcode: 21274
Abstract:Entropy methods coupled to nonlinear diffusions are powerful tools to study some functional inequalities of Sobolev type. Self-similar solutions can indeed be reinterpreted as optimal Aubin-Talenti solutions. A notion of generalized entropy is the key tool which relates the nonlinear regime to the linearized problem around the asymptotic profile and reduces the analysis to a spectral problem. Estimates can be made constructive. This gives quantitative stability results with explicit constants, under constraints. Entropy methods can be compared with other direct methods, intended for instance to obtain bounds on the stability constant in the Bianchi-Egnell stability result for the Sobolev inequality. In many cases, better estimates are obtained using entropy methods, but this often comes to the price of a restriction on the functional space.