On a quadratic gradient natural term for the Pucci extremal operators

2024/11/02 by de Oliveira, José Francisco, Ó, João Marcos do, Ubilla, Pedro +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.01087

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.

Cited by

• Existence and a priori bounds for fully nonlinear PDEs with a harmonic map-like structure

Related

• Representation Formula for Viscosity Solution to a PDE Problem involving Pucci's Extremal Operator
• Lyapunov type inequality for extremal Pucci's equations
• Oscillating solutions for nonlinear equations involving the Pucci's extremal operators
• Radial solutions for Hénon type fully nonlinear equations in annuli and exterior domains
• Super-linear elliptic equation for the Pucci operator without growth restrictions for the data