An Agmon-Allegretto-Piepenbrink principle for Schrödinger operators.

IF 1.8 2区数学 Q1 MATHEMATICS

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas 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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薛定谔算子的阿格蒙-阿列格雷托-皮彭布林克原理

我们证明，每个 Borel 函数 V ：Ω → [ - ∞ , + ∞ ] 定义在开放子集 Ω ⊂ R N 上，会诱导一个分解 Ω = S∪ ⋃ i D i，使得 W 0 1 , 2 ( Ω ) ∩ L 2 ( Ω ；V + d x ) 在 S 上几乎处处为零，并且在每个分量 D i 上存在 - Δ + V 的非负超解，从而得到相关二次型 ∫ D i ( |∇ ξ | 2 + V ξ 2 ) 的非负性。.

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来源期刊

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas 数学-数学

CiteScore

4.70

自引率

17.20%

发文量

151

审稿时长

>12 weeks

期刊介绍： The journal publishes, in English language only, high-quality Research Articles covering Algebra; Applied Mathematics; Computational Sciences; Geometry and Topology; Mathematical Analysis; Statistics and Operations Research. Also featured are Survey Articles in every mathematical field.