Calculus of Variations and Geometric Measure Theory
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A. Goffi

Some new Liouville-type results for fully nonlinear PDEs on the Heisenberg group

created by goffi on 19 Feb 2020
modified on 20 Jun 2020

[BibTeX]

Accepted Paper

Inserted: 19 feb 2020
Last Updated: 20 jun 2020

Journal: Nonlinear Analysis
Volume: 200
Year: 2020
Doi: 10.1016/j.na.2020.112013

ArXiv: 2002.06422 PDF

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.

Keywords: Heisenberg group, Liouville Theorem, Fully nonlinear equations, Nonlinear degenerate elliptic equations, Hadamard Three-Sphere theorem


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