Allen-Cahn equation for the truncated Laplacian: Unusual phenomena

Abstract

We study entire viscosity solutions of the Allen-Cahn type equation for the truncated Laplacian that are either one dimensional or radial, in order to shed some light on a possible extension of the Gibbons conjecture in this degenerate elliptic setting.

Keywords

• fully nonlinear degenerate elliptic equations
• entire solutions
• one dimensional symmetry