On a Natural Quadratic Gradient Term for the Pucci Extremal Operators

Journal of Geometric Analysis 2026 Open access

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Authors: José Francisco de Oliveira, João Marcos Ó, Abiel Costa Macedo, Pedro Ubilla
DOI: 10.1007/s12220-026-02359-3
Cited by: 0
References: 32

Abstract

Abstract We introduce a quadratic gradient type term for the Pucci extremal operators. Our analysis demonstrates that this proposed term extends the classical quadratic gradient term associated with the Laplace equation, and we investigate the impact of the Kazdan-Kramer transformation. As an application, we explore the existence, non-existence, uniqueness, Liouville-type results, and asymptotic behavior of solutions for the new class of Pucci equations under various conditions on both nonlinearity and domains.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Numerical methods in inverse problems Advanced Mathematical Modeling in Engineering

Publication details

Journal / source
Journal of Geometric Analysis
Publisher
Springer Science and Business Media LLC
Volume
36
Issue
4
Publication date
7 March 2026
Language
EN