一类线性椭圆方程的高阶导数估计  

Higher Derivative Estimates for a Linear Elliptic Equation

作　　者：王明 WANG Ming(School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]中国地质大学数理学院,湖北武汉430074

出　　处：《应用数学》2022年第3期701-707,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(12171442)。

摘　　要：众所周知,如果位势函数V是解析的,则椭圆方程△u=Vu的解是解析的.但是,如果V是超解析的,则对该解的超解析性知之甚少.在本文中,我们通过利用精巧的数学归纳法,证明了该解具有对数型超解析定量估计.It is well known that the solution of the elliptic equationΔu=Vu is analytic if the potential V is analytic.But little is known on the ultra analyticity of the solution if V is ultra analytic.In this note,we show that the solution enjoys a log type ultra analyticity bound by an elegant and delicate induction argument.

关 键 词：椭圆方程 解析性 高阶导数 

分 类 号：O175.25[理学—数学] O174.55[理学—基础数学]