@Article{ATA-35-66,
author = {Hua Chen, Hongge Chen, Junfang Wang and Nana Zhang},
title = {Lower Bounds of Dirichlet Eigenvalues for General Grushin Type Bi-Subelliptic Operators},
journal = {Analysis in Theory and Applications},
year = {2019},
volume = {35},
number = {1},
pages = {66--84},
abstract = {<p style="text-align: justify;">Let $\Omega$ be a bounded open domain in ${\mathbb{R}}^{n}$ with smooth boundary $\partial \Omega$. Let $X=(X_{1},X_{2},\cdots,X_{m})$ be a system of general Grushin type vector fields defined on $\Omega$ and the boundary $\partial\Omega$ is non-characteristic for $X$. For $\Delta _{X}=\sum_{j=1}^mX_j^2$, we denote $\lambda_{k}$ as the $k$-th eigenvalue for the bi-subelliptic operator $\Delta _{X}^2$ on $\Omega$. In this paper, by using the sharp sub-elliptic estimates and maximally hypoelliptic estimates, we give the optimal lower bound estimates of $\lambda_k$ for the operator $\Delta _{X}^2$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-0002},
url = {http://global-sci.org/intro/article_detail/ata/13092.html}
}