Symmetry results for nonlinear elliptic operators with unbounded drift

TL;DR

This paper proves one-dimensional symmetry of solutions to certain nonlinear elliptic equations with unbounded drift, under energy conditions, regardless of the space dimension.

Contribution

It establishes symmetry results for nonlinear elliptic operators with unbounded drift without restrictions on the ambient space dimension.

Findings

Solutions are one-dimensional under energy conditions.

Results apply in any space dimension.

No restrictions on the dimension of the ambient space.

Abstract

We prove the one-dimensional symmetry of solutions to elliptic equations of the form $-\dive(e^{G(x)}a(|\nabla u|)\nabla u)=f(u) e^{G(x)}$, under suitable energy conditions. Our results hold without any restriction on the dimension of the ambient space.