On the equation $Du+Xu=0$ and its relation to Schroedinger ground states

Abstract

We present some simple relations between the absolute minimizers of the functional $||Du+Xu||$, where $X$ is a vector field on $R^n$, and ground state solutions to the (non-relativistic) Schroedinger equation. This article is a byproduct of the study of the more general functional $||ADu+F^{\prime }(u)X||$.