现在位置:首页 > 学术报告
 

 

Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Professor Chen Hua,School of Mathematics and Statistics, Wuhan University

Inviter:  
Title:
Estimates of Dirichlet Eigenvalues for Degenerate Elliptic Operators
Time & Venue:
2015.8.28 16:00-17:00 N902
Abstract:
Let $\Omega$ be a bounded open domain in $R^n$ with smooth boundary and $X=(X_1, X_2, \cdots, X_m)$ be a system of real smooth vector fields defined on $\Omega$ with the boundary $\partial\Omega$ which is non-characteristic for $X$. If $X$ satisfies the H\"ormander's condition, then the vector fields is finite degenerate and the sum of square operator $\triangle_{X}=\sum_{j=1}^{m}X_j^2$ is a finitely degenerate elliptic operator, otherwise the operator $-\triangle_{X}$ is called infinitely degenerate. If $\lambda_j$ is the $j^{th}$ Dirichlet eigenvalue for $-\triangle_{X}$ on $\Omega$, then this paper shall study the lower bound estimates for $\lambda_j$. Firstly, by using the sub-elliptic estimate directly, we shall give a simple lower bound estimates of $\lambda_j$ for general finitely degenerate $\triangle_{X}$ which is polynomial increasing in $j$. Secondly, if $\triangle_{X}$ is so-called Grushin type degenerate elliptic operator, then we can give a precise lower bound estimates for $\lambda_j$. Finally, by using logarithmic regularity estimate, for infinitely degenerate elliptic operator $\triangle_{X}$ we prove that the lower bound estimates of $\lambda_j$ will be logarithmic increasing in $j$.
 

 

附件下载:
 
 
【打印本页】【关闭本页】
电子政务平台   |   科技网邮箱   |   ARP系统   |   会议服务平台   |   联系我们   |   友情链接