On the uniqueness problem for Dirichlet operators
type: Item
instance of: scholarly article
title: On the uniqueness problem for Dirichlet operators
zbMATH Open document ID: 0942.35054
published in: Journal of Functional Analysis
publication date: 2000-08-14T00:00:00Z
review text: In this paper the author deals with the uniqueness problem for the classical Dirichlet form on a weighted real \(L^2\)-space when the underlying space is finite dimensional. The paper establish a criterion of strong uniqueness for the Dirichlet operator under local assumptions on the logarithmic derivative generalizing preceding results. The problem is reduced to the essential selfadjointness of a degenerate Dirichlet operator whose coefficients vanish outside a ball. Then the essential selfadjointness is proved for the operator on the ball using a method of a-priori estimates which turns out to be applicable for the situations with degeneracy. Next the uniqueness problem is considered in \(L^1\).
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 1270894
zbMATH Keywords: Dirichlet operators
zbMATH Keywords: uniqueness
author: V. A. Liskevich
reviewed by: Marco Codegone
MaRDI profile type: Publication
full work available at URL: jfan.1998.3365
OpenAlex ID: W2023738493
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DOI: 10.1006/JFAN.1998.3365
description: scientific article; zbMATH DE number 1270894