Homogeneous solutions of extremal Pucci's equations in planar cones

TL;DR

This paper derives explicit homogeneous solutions for Pucci's extremal equations in planar cones, enabling new monotonicity formulas and precise non-existence conditions for Liouville-type solutions.

Contribution

It provides the first explicit expressions of homogeneous solutions in 2D cones for Pucci's equations, advancing understanding of their structure and applications.

Findings

Explicit solutions for Pucci's equations in 2D cones.

Monotonicity formulas for nonnegative supersolutions.

Necessary and sufficient conditions for Liouville-type non-existence.

Abstract

We derive explicit expressions of the homogeneous solutions in two dimensional cones for Pucci's extremal equations. As examples of possible applications, we obtain monotonicity formulas for all nonnegative supersolutions and necessary and sufficient explicit conditions for non--existence results of Liouville type.