Principal Frequency of -Sub-Laplacians for General Vector Fields
Michael Ruzhansky
Ghent University, Belgium and Queen Mary University of London, UKBolys Sabitbek
Queen Mary University of London, UK, and Al Farabi Kazakh National University, Almaty, KazakhstanDurvudkhan Suragan
Nazarbayev University, Nursultan, Kazakhstan
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Abstract
In this paper, we prove the uniqueness and simplicity of the principal frequency (or the first eigenvalue) of the Dirichlet -sub-Laplacian for general vector fields. As a byproduct, we establish the Caccioppoli inequalities and also discuss the particular cases on the Grushin plane and on the Heisenberg group.
Cite this article
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan, Principal Frequency of -Sub-Laplacians for General Vector Fields. Z. Anal. Anwend. 40 (2021), no. 1, pp. 97–109
DOI 10.4171/ZAA/1674