An Agmon-Allegretto-Piepenbrink principle for Schrödinger operators.

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 Epub Date: 2022-07-13 DOI:10.1007/s13398-022-01293-7

Stefano Buccheri, Luigi Orsina, Augusto C Ponce

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引用次数: 0

Abstract

We prove that each Borel function $V : Ω \to [- \infty, + \infty]$ defined on an open subset $Ω \subset R^{N}$ induces a decomposition $Ω = S \cup ⋃_{i} D_{i}$ such that every function in $W_{0}^{1, 2} (Ω) \cap L^{2} (Ω; V^{+} d x)$ is zero almost everywhere on S and existence of nonnegative supersolutions of $- Δ + V$ on each component $D_{i}$ yields nonnegativity of the associated quadratic form $\int_{D_{i}} {(| \nabla ξ |}^{2} + V ξ^{2}) .$ .

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Schrödinger算子的Agmon-Allegretto-Piepenbrink原理。

我们证明了定义在开放子集上的每个Borel函数V: Ω→[-∞，+∞]Ω∧R N推导出一个分解Ω = S∪i D i，使得w0 1,2 (Ω)∩l2 (Ω;V + d x)在S上几乎处处为零，并且- Δ + V在每个分量上的非负超解的存在产生了相关二次形式∫d1 (| ξ | 2 + V ξ 2)的非负性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.