Uniqueness of Schrödinger operators restricted in a domain
type: Item
instance of: scholarly article
title: Uniqueness of Schrödinger operators restricted in a domain
zbMATH Open document ID: 0913.35035
published in: Journal of Functional Analysis
publication date: 1999-06-10T00:00:00Z
review text: The author considers an (open) domain \(D\) in \(\mathbb{R}^n\) with boundary \(\partial D\). Let \(C^\infty_0(D)\) be the space of all differentiable real functions on \(D\) with compact support. He considers the Schrödinger operator \(S:(-\Delta/2+ V, C^\infty_0(D))\), where \(V:D\to \mathbb{R}\) is a Borel measurable potential. The essential self-adjointness of \(S\) in \(L^2(D,dx)\) is equivalent to the uniqueness of the self-adjoint extension of \(S\) or the unique solvability of Schrödinger's equations in \(L^2(D)\), which has been studied by Kato, Reed and Simon and others. The main results and related works are studied in the first section. Some preliminaries and lemmas are given in section 2. The proofs of the lemmas and theorems are given in section 3, 4, 5. Some applications to the unique solvability of partial differential equations are presented in section 6. Finally, several interesting counterexamples and examples are presented in section 7.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 1215686
zbMATH Keywords: Markovian self-adjointness
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: essential self-adjointness
zbMATH Keywords: unique solvability
author: Liming Wu
MaRDI profile type: Publication
full work available at URL: jfan.1997.3181
OpenAlex ID: W2080740125
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DOI: 10.1006/JFAN.1997.3181
description: scientific article; zbMATH DE number 1215686