An Agmon-Allegretto-Piepenbrink principle for Schrödinger operators
(2022) Real Academia de Ciencias Exactas, Fisicas y Naturales. Revista. Serie A, Matematicas — Vol. 116, n° 4, p. 151 (2022)
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- Abstract
- We prove that each Borel function $V\colon \Omeg \to [-\infty,+\infty]$ defined on an open subset $\Omega \subset \mathbb{R}^N$ induces a decomposition $\Omega=S\cup\Bigcup_i D_i$ such that every function in $W{1.2}_0 (\Omega)\capL^2(\Omega;V^+dx) $ is zero almost everywhere on $S$ and existence of nonnegative supersolutions of $-\Delta+V$ on each component $D_i$ yields nonnegativity of the associated quadratic form $/int_{D_i} (|\nabla \xi|^2+V\xi^2)$.
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Citations
Buccheri, S., Orsina, L., & Ponce, A. (2022). An Agmon-Allegretto-Piepenbrink principle for Schrödinger operators. Real Academia de Ciencias Exactas, Fisicas y Naturales. Revista. Serie A, Matematicas, 116(4), 151. https://doi.org/10.1007/s13398-022-01293-7 (Original work published 2022)