JournalszaaVol. 40, No. 1pp. 97–109

Principal Frequency of -Sub-Laplacians for General Vector Fields

  • Michael Ruzhansky

    Ghent University, Belgium and Queen Mary University of London, UK

  • Bolys Sabitbek

    Queen Mary University of London, UK, and Al Farabi Kazakh National University, Almaty, Kazakhstan

  • Durvudkhan Suragan

    Nazarbayev University, Nursultan, Kazakhstan
Principal Frequency of $p$-Sub-Laplacians for General Vector Fields cover

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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