The generalized Elvis problem: Solving minimal time problems in anisotropic mediums

The Elvis problem was introduced into the undergraduate mathematical literature by Timothy Pennings[1] whose dog (named Elvis) enjoyed fetching an object thrown from the shore of Lake Michigan into the water. Elvis was observed to retrieve the object by going in a path that resembled how light would refract in isotropic mediums according to Snell’s Law. We retain the problem’s "Elvis" nomenclature but greatly generalize the problem by considering anisotropic mediums and use the tools of Convex Analysis to provide a complete description of optimal movement. The velocity sets are closed, bounded convex sets containing the origin in its interior, whereas the original problem used only centered balls. Further generalizations are considered with faster movement allowed on the interface and with more than two mediums.