We prove Liouville type results for non-negative solutions of the differential inequality Δφu⩾f(u)ℓ(|∇0u|) on the Heisenberg group under a generalized Keller-Osserman condition. The operator Δφu is the φ-Laplacian defined by div0(|∇0u|−1φ(|∇0u|)∇0u) and φ, f and ℓ satisfy mild structural conditions. In particular, ℓ is allowed to vanish at the origin. A key tool that can be of independent interest is a strong maximum principle for solutions of such differential inequality.'

Liouville type results and a maximum principle for non-linear differential operators on the Heisenberg group

BRANDOLINI, Luca;MAGLIARO, Marco
2014-01-01

Abstract

We prove Liouville type results for non-negative solutions of the differential inequality Δφu⩾f(u)ℓ(|∇0u|) on the Heisenberg group under a generalized Keller-Osserman condition. The operator Δφu is the φ-Laplacian defined by div0(|∇0u|−1φ(|∇0u|)∇0u) and φ, f and ℓ satisfy mild structural conditions. In particular, ℓ is allowed to vanish at the origin. A key tool that can be of independent interest is a strong maximum principle for solutions of such differential inequality.'
journal article - articolo
2014
Brandolini, Luca; Magliaro, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/32634
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