Essential self-adjointness of second-order elliptic operator with measurable coefficients
type: Item
instance of: scholarly article
title: Essential self-adjointness of second-order elliptic operator with measurable coefficients
zbMATH Open document ID: 0597.35029
DOI: 10.1007/BF01059712
author: B. George
published in: Ukrainian Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: Let us consider the matrix \((a_{kj}(x))\), \(k,j=1,...,\ell\), the elements of which are real measurable functions in \({\mathbb{R}}^{\ell}\) satisfying \[ a_{kj}(x)=a_{jk}(x),\quad \sum_{j}\xi^ 2_ j=\sum_{k,j}a_{kj}(x)\xi_ k\xi_ j, \] for all \(\xi \in {\mathbb{R}}^{\ell}\) and almost all \(x\in {\mathbb{R}}^{\ell}\). There is proved the essential self-adjointness of \[ L=-\sum_{k,j}(\partial /\partial x_ k)a_{kj}(x)\partial /\partial x_ j+V,\quad V\in L^ 2,\quad V\geq 0. \] This is the first result in this direction if \(\ell \geq 4\) and the coefficients \(a_{kj}\) are locally unbounded functions.
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3962265
zbMATH Keywords: Friedrichs regularization
zbMATH Keywords: Hölder inequality
zbMATH Keywords: measurable functions
zbMATH Keywords: essential self-adjointness
MaRDI profile type: Publication
cites work: A canonical decomposition for quadratic forms with applications to monotone convergence theorems
cites work: Q5526485
cites work: Q5632974
cites work: Schrödinger operators with singular magnetic vector potentials
cites work: Finiteness of the rate of propagation of perturbations for hyperbolic equations
cites work: Self-adjointness of the minimal Schrödinger operator with potential belonging to \(L_{1,\text{loc}}\)
description: scientific article; zbMATH DE number 3962265