In this paper, we present exact missing terms for the Poincaré inequalities on homogeneous groups. We also discuss some consequences in the Euclidean cases. Thus, we have succeeded in finding a simple proof of the sharp Poincaré inequality for the Dirichlet Laplacian.
The authors were supported in parts by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. No new data was collected or generated during the course of this research.
"Poincaré inequalities with exact missing terms on homogeneous groups." J. Math. Soc. Japan 73 (2) 497 - 503, April, 2021. https://doi.org/10.2969/jmsj/83738373