応用解析研究会 2026 年度講演一覧

第 883 回 4 月 4 日（土） 15:30～
- 講演者: 三竹大寿（早稲田大学）
- 講演題目: ノイマン境界条件におけるハミルトン・ヤコビ方程式の粘性解の最適分数冪半凸性
- 場所: 早稲田大学西早稲田キャンパス 55 号館 N 棟 2階物理学科・応用物理学科会議室

第 884 回 4 月 11 日（土） 15:30～
- 講演者: Prasun Roychowdhury（早稲田大学）
- 講演題目: Stability of Higher-order Hardy Inequalities for Baouendi-Grushin Vector Fields
- 講演概要: In this talk, I will present a unified framework for deriving and improving Hardy, Rellich, and Hardy-Rellich inequalities related to the Baouendi-Grushin operator, emphasizing both identity-based techniques and stability analysis. In the first part, we explore sharp inequalities and identities for the Grushin operator using spherical harmonics and the Bessel pair approach. In the second part, we analyze the extremizer stability of higher-order Hardy-Rellich inequalities in the radial Grushin setting. By connecting subcritical and critical inequalities through explicit identities, we derive sharp remainder terms and establish quantitative stability estimates via extremal profile approximations. These findings contribute to both the structural understanding of Grushin-type operators and the development of refined functional inequalities in degenerate settings.
- 場所: 早稲田大学西早稲田キャンパス 55 号館 N 棟 1階 01-02-3室