Removable singularities for degenerate elliptic Pucci operators

TL;DR

This paper introduces new nonlinear second-order operators related to eigenvalues of the Hessian, aiming to extend maximum principles and removable singularity results to highly degenerate elliptic cases.

Contribution

It defines weighted eigenvalue-based operators and extends classical results to degenerate elliptic operators in geometric contexts.

Findings

Established maximum principles for new operators

Proved removable singularities under degeneracy conditions

Extended classical elliptic theory to degenerate cases

Abstract

In this paper we introduce some fully nonlinear second order operators defined as weighted partial sums of the eigenvalues of the Hessian matrix, arising in geometrical contexts, with the aim to extend maximum principles and removable singularities results to cases of highly degenerate ellipticity.nn