The paper focuses on the Lp-Positivity Preservation property (Lp-PP for short) on a Riemannian manifold (M,g). It states that any Lp function u with 1<+∞, which solves (−Δ+1)u≥0 on M in the sense of distributions must be non-negative. Our main result is that the Lp-PP holds if (the possibly incomplete) M has a finite number of ends with respect to some compact domain, each of which is q-parabolic for some, possibly different, values 2p/(p−1)

Pigola, S., Valtorta, D., Veronelli, G. (2024). Approximation, regularity and positivity preservation on Riemannian manifolds. NONLINEAR ANALYSIS, 245(August 2024) [10.1016/j.na.2024.113570].

Approximation, regularity and positivity preservation on Riemannian manifolds

Pigola, S;Valtorta, D
;
Veronelli, G
2024

Abstract

The paper focuses on the Lp-Positivity Preservation property (Lp-PP for short) on a Riemannian manifold (M,g). It states that any Lp function u with 1<+∞, which solves (−Δ+1)u≥0 on M in the sense of distributions must be non-negative. Our main result is that the Lp-PP holds if (the possibly incomplete) M has a finite number of ends with respect to some compact domain, each of which is q-parabolic for some, possibly different, values 2p/(p−1)
Articolo in rivista - Articolo scientifico
Lp positivity preservation; Removable singularities; Spectral theory;
English
18-mag-2024
2024
245
August 2024
113570
open
Pigola, S., Valtorta, D., Veronelli, G. (2024). Approximation, regularity and positivity preservation on Riemannian manifolds. NONLINEAR ANALYSIS, 245(August 2024) [10.1016/j.na.2024.113570].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/478979
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