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- Title
New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs.
- Authors
Bardi, Martino; Goffi, Alessandro
- 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 Hörmander 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 Hörmander vector fields.
- Subjects
MAXIMUM principles (Mathematics); VECTOR fields; HAMILTON-Jacobi-Bellman equation; ELLIPTIC equations; MAXIMA &; minima
- Publication
Calculus of Variations & Partial Differential Equations, 2019, Vol 58, Issue 6, pN.PAG
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-019-1620-2