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A note on the inverse maximum principle on Carnot groups

D’Ambrosio, Lorenzo
•
Gallo, Marco
2025
  • Controlled Vocabulary...

Abstract
Let ΔG be a sublaplacian on a Carnot group, and let μ be a local measure on the open set Ω ⊂ G. If u ∈ L1l oc(Ω) is such that −ΔGu = μ, u ≥ 0 on Ω, then μc ≥ 0, where μc is the concentrated component of μ with respect to the G-capacity. This extends to the Carnot group setting a result contained in [9].
DOI
10.13137/2464-8728/37091
Soggetti
  • Maximum principles

  • Carnot groups

  • sublaplacian

  • measure data

  • capacity

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