Non-classical Solution to Hessian Equation from Cartan Isoparametric Cubic

TL;DR

This paper constructs a non-smooth solution to a fully nonlinear Hessian equation using the Cartan isoparametric cubic in five dimensions, expanding understanding of solutions to elliptic equations.

Contribution

It introduces a novel method to generate non-smooth solutions to Hessian equations via Cartan isoparametric cubics, a new approach in the field.

Findings

Constructed a non-smooth solution to Hessian equations

Utilized Cartan isoparametric cubic in 5D

Advances understanding of elliptic PDE solutions

Abstract

We show how to construct a non-smooth solution to Hessian fully nonlinear second-order uniformly elliptic equation using the Cartan isoparametric cubic in 5 dimensions.