Regularity theory and Liouville-type results for viscosity solutions to the false mean curvature equation. ‎

In this talk, we revisit some classical Liouville-type results in half spaces for uniformly elliptic equations. We extend these results to the nonuniformly elliptic equations known as false mean curvature equations. The regularity theory of locally Lipschitz viscosity solutions will also be addressed. ‎