Remarks on the Pogorelov type estimate for the degenerate $k$-Hessian equation

TL;DR

This paper explores a new condition on the right-hand side of the degenerate $k$-Hessian equation to derive Pogorelov type estimates, advancing understanding of solutions under degeneracy.

Contribution

It introduces a novel condition on the degenerate right-hand side $f$ that enables Pogorelov type estimates for the $k$-Hessian equation.

Findings

Established Pogorelov type estimates under the new condition

Extended the applicability of estimates to degenerate cases

Provided theoretical insights into the structure of solutions

Abstract

This paper investigates the Pogorelov type estimate for the $k$-Hessian equation under a new condition on the degenerate right-hand side $f$.