What does this research mean for the field?

A new quadratic gradient term for the Pucci extremal operators extends the classical quadratic gradient term associated with the Laplace equation and influences the existence and uniqueness of solutions for a new class of Pucci equations. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The main aim is to propose a quadratic gradient term for Pucci extremal operators and analyze its properties.

March 8, 2026Open Access

On a Natural Quadratic Gradient Term for the Pucci Extremal Operators

Key Points

The main aim is to propose a quadratic gradient term for Pucci extremal operators and analyze its properties.
Introduced a quadratic gradient term for the Pucci extremal operators.
Analyzed the effects of the Kazdan-Kramer transformation on this new term.
Investigated existence, non-existence, uniqueness, and asymptotic behavior of Pucci equations under specific conditions.
Demonstrated that the new quadratic term extends classical gradient terms related to the Laplace equation.
Identified conditions for existence and non-existence of solutions for the new Pucci equations.
Established uniqueness and Liouville-type results for certain scenarios.

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.

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Discussion

Cite this study

Oliveira et al. (Sat,) studied this question.

www.synapsesocial.com/papers/69ada90bbc08abd80d5bc6ed — DOI: https://doi.org/10.1007/s12220-026-02359-3

Authors

José Francisco de Oliveira

João Marcos do Ó

Abiel Costa Macedo

Journals

Journal of Geometric Analysis

Actions

References and Citations

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Building similarity graph...

Analyzing shared references across papers

On a Natural Quadratic Gradient Term for the Pucci Extremal Operators

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

Authors

Journals

Actions

References and Citations

Citation Network

Connected Papers

Discussion