Prasun Roychowdhury (Milano)
Abstract: In this talk, I will present a unified framework for deriving and improving Hardy, Rellich, and Hardy–Rellich inequalities associated with 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 both to the structural understanding of Grushin-type operators and to the development of refined functional inequalities in degenerate settings.
