Let ∆_G be a sublaplacian on a Carnot group, and let μ be a local measure on the open set Ω ⊂ G. If u ∈ L^1_{loc}(Ω) is such that −∆_Gu = μ, u ≥ 0 on Ω, then μ_c ≥ 0, where μ_c is the concentrated component of μ with respect to the G-capacity. This extends to the Carnot group setting a result contained in [9].
A note on the inverse maximum principle on Carnot groups
Lorenzo D’Ambrosio
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2024-01-01
Abstract
Let ∆_G be a sublaplacian on a Carnot group, and let μ be a local measure on the open set Ω ⊂ G. If u ∈ L^1_{loc}(Ω) is such that −∆_Gu = μ, u ≥ 0 on Ω, then μ_c ≥ 0, where μ_c is the concentrated component of μ with respect to the G-capacity. This extends to the Carnot group setting a result contained in [9].File in questo prodotto:
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