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)
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