Published Paper

Inserted: 12 feb 2019
Last Updated: 23 sep 2021

Journal: Calc. Var. Partial Differential Equations
Volume: 58
Number: no. 184
Pages: 20
Year: 2019
Doi: 10.1007/s00526-019-1620-2

Abstract:

We introduce a notion of subunit vector field for fully nonlinear degenerate elliptic equations. We prove that an interior maximum of a viscosity subsolution of such an equation propagates along the trajectories of subunit vector fields. This implies strong maximum and minimum principles when the operator has a family of subunit vector fields satisfying the H\"ormander condition. In particular these results hold for a large class of nonlinear subelliptic PDEs in Carnot groups. We prove also a strong comparison principle for degenerate elliptic equations that can be written in Hamilton-Jacobi-Bellman form, such as those involving the Pucci's extremal operators over H\"ormander vector fields.

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