@article{15b67a9faaa8486bb80fcd87dff5d857,
title = "Principal frequency of p-sub-Laplacians for general vector fields",
abstract = "In this paper, we prove the uniqueness and simplicity of the principal frequency (or the first eigenvalue) of the Dirichlet p-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.",
keywords = "Caccioppoli inequality, P-sub-Laplacian, Picone{\textquoteright}s identity, Principal frequency, Smooth manifold",
author = "Michael Ruzhansky and Bolys Sabitbek and Durvudkhan Suragan",
note = "Funding Information: Acknowledgement. The first author was supported by FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and EPSRC grant EP/R003025/1. The second author was supported in parts by EPSRC grant EP/R003025/1 and the MES RK grant AP08053051 . The third author was supported by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. Publisher Copyright: {\textcopyright} European Mathematical Society Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
doi = "10.4171/ZAA/1674",
language = "English",
volume = "40",
pages = "97--109",
journal = "Zeitschrift fur Analysis und ihre Anwendung",
issn = "0232-2064",
publisher = "Heldermann Verlag",
number = "1",
}