On ABP Estimates for a Class of Fully Nonlinear Singular-Degenerate Elliptic Equations and Applications
Year: 2026
Type: preprint
Abstract: We establish an Alexandrov-Bakelman-Pucci type estimate for a class of fully nonlinear elliptic equations with singular or degenerate coefficients and nonlinear dependence on the gradient. The estimate bounds sub-solutions in terms of their boundary values and weighted integrals of the data. It holds for classical sub-solutions and for viscosity sub-solutions with locally Lipschitz gradients. The assumptions allow general rates of growth in the gradient, with a smallness condition on the data when the associated gradient weight has finite integral. The proof uses the classical weighted contact-set argument. As applications, we obtain sup-norm estimates for viscosity sub-solutions to a class of generalized Monge-Ampère equations, Hessian equations, Hessian quotients under an additional condition on the contact Hessian, and anisotropic mean-curvature-type equations.
Source: arXiv (Cornell University)
Authors: Fang, Junyuan, Peltier, Jack, Phan, Tuoc
Institutions: Brown University, University of Tennessee at Knoxville
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223235252