Eigenvalue Gap Theorems for a Class of Nonsymmetric Elliptic Operators on Convex Domains
Eigenvalue Gap Theorems for a Class of Nonsymmetric Elliptic Operators on Convex Domains
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DOI：
10.1080/03605302.2014.978014
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发表时间：
2012-12
影响因子：
1.9
通讯作者：
J. Wolfson
中科院分区：
文献类型：
--
作者：
J. Wolfson
采用Andrews-Clutterbuck方法，我们证明了欧氏空间凸域上一类非对称二阶线性椭圆算子的特征值间隙定理。算子类包括具有势的 Bakry-Emery 拉普拉斯算子和任何具有二阶项的拉普拉斯算子，其一阶项具有在开域中具有紧支持的系数。特征值间隙的边界是闭区间上相关 Sturm-Liouville 问题的间隙。
Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery laplacian with potential and any operator with second order term the laplacian whose first order terms have coefficients with compact support in the open domain. The eigenvalue gap is bounded below by the gap of an associated Sturm-Liouville problem on a closed interval.