We prove new (sharp) Liouville-type properties via degenerate Hadamard three-sphere theorems for fully nonlinear equations structured over Heisenberg vector fields. As model examples, we cover the case of Pucci's extremal operators perturbed by suitable semilinear and gradient terms, extending to the Heisenberg setting known contributions valid in the Euclidean framework.
Some new Liouville-type results for fully nonlinear PDEs on the Heisenberg group / Goffi A.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - ELETTRONICO. - 200:(2020), pp. 112013.0-112013.0. [10.1016/j.na.2020.112013]
Some new Liouville-type results for fully nonlinear PDEs on the Heisenberg group
Goffi A.
2020
Abstract
We prove new (sharp) Liouville-type properties via degenerate Hadamard three-sphere theorems for fully nonlinear equations structured over Heisenberg vector fields. As model examples, we cover the case of Pucci's extremal operators perturbed by suitable semilinear and gradient terms, extending to the Heisenberg setting known contributions valid in the Euclidean framework.
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