In this paper we consider fully nonlinear second-order elliptic partial differential equa- tions, with measurable, possibly singular and unbounded lower order coefficients, in unbounded domains of Rn. We prove the Alexandroff–Bakelman–Pucci maximum principle for Lp − viscosity solutions under suitable assumptions on the geometry f domains, satisfied by a class of very large unbounded domains including the complement of hypersurfaces, such as the cut plane in dimension n = 2 and the closure of (n − 1)- dimensional open convex cones in higher dimensions, as well as their subdomains.
ABP Estimates for Viscosity Solutions of Elliptic Equations with Unbounded Coefficients in Large Domains
P. Di Gironimo;A. Vitolo
2026
Abstract
In this paper we consider fully nonlinear second-order elliptic partial differential equa- tions, with measurable, possibly singular and unbounded lower order coefficients, in unbounded domains of Rn. We prove the Alexandroff–Bakelman–Pucci maximum principle for Lp − viscosity solutions under suitable assumptions on the geometry f domains, satisfied by a class of very large unbounded domains including the complement of hypersurfaces, such as the cut plane in dimension n = 2 and the closure of (n − 1)- dimensional open convex cones in higher dimensions, as well as their subdomains.File in questo prodotto:
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