The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators
type: Item
instance of: scholarly article
title: The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators
zbMATH Open document ID: 0891.35025
author: Yoshinori Morimoto
author: Tatsushi Morioka
published in: Bulletin des Sciences Mathématiques
publication date: 1997-12-18T00:00:00Z
review text: At the beginning of the paper, the authors give rather a wide review of the results obtained by different authors in the investigation of the hypoellipticity of second-order infinitely degenerate elliptic operators and indicate the equivalence of various conditions. They prove that if in a segment of the finite interval in \(\mathbb{R}_x\) the functions are \(f>0\) and \(g>0\), then the operator \[ P= D^2_x+ f(x)D^2_t+ g(x)D^2y\quad\text{in }\mathbb{R}^3_{x,t,y} \] is hypoelliptic if and only if \(f\) and \(g\) satisfy a certain reduction condition. An analogous result is proved for a multivariable operator \(P\), where \(x\in\mathbb{R}^n_x\), \(t\in \mathbb{R}^k_t\), \(y\in\mathbb{R}^n_y\). In addition, some estimates are obtained that are applied to value estimates for Schrödinger operators.
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 1098582
zbMATH Keywords: infinitely degenerate elliptic operators
reviewed by: Bronius Kvedaras
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1098582