Sharp remainder of the Poincaré inequality for Baouendi-Grushin vector fields
Suragan D. Yessirkegenov N.
1 March 2023World Scientific
Asian-European Journal of Mathematics
2023#16Issue 3
In this note, we establish a sharp remainder formula for the Poincaré inequality for the Baouendi-Grushin vector fields. We give a simple proof for it without using the variational principle. As an application, we obtain a blow-up result for solutions to the Dirichlet initial-boundary value problem for the Baouendi-Grushin heat operator.
Baouendi-Grushin operator , blow-up solution , eigenfunction , Poincaré inequalitiy
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Department of Mathematics, Nazarbayev University, Kazakhstan
Suleyman Demirel University, Kaskelen, Kazakhstan
Department of Mathematics
Suleyman Demirel University
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