Sharp remainder of the L^p-Poincaré inequality for Baouendi-Grushin vector fields

2025/07/02 by Apseit, Kuralay, Yessirkegenov, Nurgissa, Zhangirbayev, Amir · 1 citation
#35A01 #35B44 #39B62 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.01681

Abstract

In this paper, we establish a sharp remainder formula for the Poincaré inequality for Baouendi-Grushin vector fields in the setting of L^p for complex-valued functions. In special cases, we recover previously known results. Consequently, we also derive the L^p-Poincaré inequality with an explicit optimal constant under a certain assumption. Additionally, we provide estimates of the remainder term for p≥2 and 1

Citations

• Bifurcation and multiplicity results for critical problems involving the p-Grushin operator
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Cited by

• Sharp remainder terms and stability of weighted Hardy-Poincaré and Heisenberg-Pauli-Weyl inequalities related to the Baouendi-Grushin operator

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• Hardy and Rellich identities and inequalities for Baouendi-Grushin operators via spherical vector fields
• Weighted Poincaré inequality and Hardy improvements related to some degenerate elliptic differential operators