scholarly journals The strong maximum principle revisited

2004 ◽  
Vol 196 (1) ◽  
pp. 1-66 ◽  
Author(s):  
Patrizia Pucci ◽  
James Serrin
Keyword(s):  
Maximum Principle ◽  
Strong Maximum Principle

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

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe 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 $$\infty $$ ∞ -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.

scholarly journals A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients

2019 ◽  
Vol 21 (07) ◽  
pp. 1850057 ◽  
Author(s):  
Francesca Anceschi ◽  
Michela Eleuteri ◽  
Sergio Polidoro
Keyword(s):  
Maximum Principle ◽  
Harnack Inequality ◽  
Weak Solutions ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Strong Maximum Principle ◽  
Kolmogorov Equation ◽  
Measurable Coefficients ◽  
Rough Coefficients ◽  
Vector Formula

We consider weak solutions of second-order partial differential equations of Kolmogorov–Fokker–Planck-type with measurable coefficients in the form [Formula: see text] where [Formula: see text] is a symmetric uniformly positive definite matrix with bounded measurable coefficients; [Formula: see text] and the components of the vector [Formula: see text] are bounded and measurable functions. We give a geometric statement of the Harnack inequality recently proved by Golse et al. As a corollary, we obtain a strong maximum principle.

Sign in / Sign up

Export Citation Format

Share Document