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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.05913 |
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| _version_ | 1866916595824066560 |
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| author | Buccheri, Stefano Orsina, Luigi Ponce, Augusto C. |
| author_facet | Buccheri, Stefano Orsina, Luigi Ponce, Augusto C. |
| contents | We prove that each Borel function $V : Ω\to [-\infty, +\infty]$ defined on an open subset $Ω\subset \mathbb{R}^{N}$ induces a decomposition $Ω= S \cup \bigcup_{i} D_{i}$ such that every function in $W^{1,2}_{0}(Ω) \cap L^{2}(Ω; V^{+} dx)$ 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 $\int_{D_{i}} (|\nabla ξ|^2+Vξ^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05913 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An Agmon-Allegretto-Piepenbrink principle for Schroedinger operators Buccheri, Stefano Orsina, Luigi Ponce, Augusto C. Analysis of PDEs Functional Analysis Primary: 35J10, 35R05, 46E35, Secondary: 35B05, 35J15, 35J20 We prove that each Borel function $V : Ω\to [-\infty, +\infty]$ defined on an open subset $Ω\subset \mathbb{R}^{N}$ induces a decomposition $Ω= S \cup \bigcup_{i} D_{i}$ such that every function in $W^{1,2}_{0}(Ω) \cap L^{2}(Ω; V^{+} dx)$ 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 $\int_{D_{i}} (|\nabla ξ|^2+Vξ^2)$. |
| title | An Agmon-Allegretto-Piepenbrink principle for Schroedinger operators |
| topic | Analysis of PDEs Functional Analysis Primary: 35J10, 35R05, 46E35, Secondary: 35B05, 35J15, 35J20 |
| url | https://arxiv.org/abs/2111.05913 |