Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations

Abstract

We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for operators of the form ${\nabla }^2\psi +L(x,\psi ,\nabla \psi )$ which are non-decreasing in $\psi$.

References in corpus (3)

• Estimates and Existence Results for some Fully Nonlinear Elliptic Equations on Riemannian Manifolds
• Asymptotic behavior of solutions to the ${\sigma }_k$-Yamabe equation near isolated singularities
• Harnack inequalities and Bôcher-type theorems for conformally invariant fully nonlinear degenerate elliptic equations

Cited by in corpus (3)

• Existence and uniqueness to a fully non-linear version of the Loewner-Nirenberg problem
• Regularity of viscosity solutions of the ${\sigma }_k$-Loewner-Nirenberg problem
• The ${\sigma }_k$-Loewner-Nirenberg problem on Riemannian manifolds for $k<\frac{n}{2}$