Existence and convexity of local solutions to degenerate hessian equations

TL;DR

This paper proves the existence of local convex solutions to degenerate Hessian equations, advancing understanding of their solvability under degeneracy conditions.

Contribution

It establishes the existence and convexity of local solutions to a class of degenerate Hessian equations, a problem previously not fully understood.

Findings

Existence of local convex solutions proven

Conditions under which solutions exist identified

Advances theoretical understanding of degenerate Hessian equations

Abstract

In this work, we prove the existence of local convex solution to the degenerate Hessian equation