Calculus of Variations and Geometric Measure Theory
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A. Goffi - F. Pediconi

A note on the strong maximum principle for fully nonlinear equations on Riemannian manifolds

created by goffi on 31 Jul 2020
modified on 17 Feb 2021


Accepted Paper

Inserted: 31 jul 2020
Last Updated: 17 feb 2021

Journal: The Journal of Geometric Analysis
Year: 2020

ArXiv: 2007.15448 PDF


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 like those modeled on the $p$- and $\infty$-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.

Keywords: degenerate elliptic equation, Riemannian manifold, Fully nonlinear equation, Hopf boundary lemma, strong maximum principle, strong comparison principle

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