We prove that each Borel function V: Ω → [- ∞, + ∞] defined on an open subset Ω ⊂ RN induces a decomposition Ω = S∪ ⋃ iDi such that every function in W01,2(Ω)∩L2(Ω;V+dx) is zero almost everywhere on S and existence of nonnegative supersolutions of - Δ + V on each component Di yields nonnegativity of the associated quadratic form ∫Di(|∇ξ|2+Vξ2).
An Agmon–Allegretto–Piepenbrink principle for Schrödinger operators / Buccheri, S.; Orsina, L.; Ponce, A. C.. - In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A, MATEMÁTICAS. - ISSN 1578-7303. - 116:4(2022). [10.1007/s13398-022-01293-7]
An Agmon–Allegretto–Piepenbrink principle for Schrödinger operators
Buccheri S.;Ponce A. C.
2022
Abstract
We prove that each Borel function V: Ω → [- ∞, + ∞] defined on an open subset Ω ⊂ RN induces a decomposition Ω = S∪ ⋃ iDi such that every function in W01,2(Ω)∩L2(Ω;V+dx) is zero almost everywhere on S and existence of nonnegative supersolutions of - Δ + V on each component Di yields nonnegativity of the associated quadratic form ∫Di(|∇ξ|2+Vξ2).File in questo prodotto:
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