We investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci's extremal operators, some singular operators such as those modeled on the p- and infinity-Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds / Goffi, A; Pediconi, F. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 31:(2021), pp. 8641-8665. [10.1007/s12220-021-00607-2]

A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

Pediconi, F
2021

Abstract

We investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci's extremal operators, some singular operators such as those modeled on the p- and infinity-Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.
31
8641
8665
Goffi, A; Pediconi, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1282345
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