Polynomial growth or decay of eigenfunctions of second-order elliptic operators
type: Item
instance of: scholarly article
title: Polynomial growth or decay of eigenfunctions of second-order elliptic operators
zbMATH Open document ID: 0656.35106
author: Jun Uchiyama
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: We study the asymptotic behaviors as \(| x| \to \infty\) of the not identically vanishing solution \(u(x)\in H^ 2_{loc}(\Omega)\) of second-order elliptic equation in an unbounded domain \(\Omega =\{x|\) \(| x| >R_ 0\}\subset R^ n\) \[ - \sum^{n}_{i,j=1}(\frac{\partial}{\partial x_ i}+\sqrt{-1}b_ i(x))a_{ij}(x)(\frac{\partial}{\partial x_ j}+\sqrt{-1}b_ j(x))u(x)+(q_ 1(x)+q_ 2(x))u(x)=0, \] where the matrix \((a_{ij}(x))\) is uniformly positive definite, \(b_ i(x)\) (1\(\leq i\leq n)\) and \(q_ 1(x)\) are real-valued functions, and \(q_ 2(x)\) is a complex-valued function.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4071514
zbMATH Keywords: polynomial growth
zbMATH Keywords: decay of eigenfunctions
zbMATH Keywords: asymptotic behaviors
zbMATH Keywords: unbounded domain
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195175868
OpenAlex ID: W1972723240
DOI: 10.2977/PRIMS/1195175868
description: scientific article; zbMATH DE number 4071514