Nonclassical Solutions of Fully Nonlinear Elliptic Equations

TL;DR

This paper demonstrates the existence of solutions that are not smooth for a class of complex nonlinear elliptic equations, expanding understanding of their solution space.

Contribution

It establishes the existence of non-smooth solutions to fully nonlinear uniformly elliptic equations, a novel result in the field.

Findings

Existence of non-smooth solutions proven

Broadens understanding of solution regularity

Implications for nonlinear elliptic PDE theory

Abstract

We prove the existence of non-smooth solutions to fully nonlinear uniformly elliptic equations.