Relaxed Energies for -Valued Maps, Nonhomogeneous Distances and Minimal Connections
Abstract: In this work, we compute the functional
defined by
where is a smooth bounded domain in and is a measurable function taking values between two positive constants a.e. in . The explicit formula involves a distance function on associated in a canonical way to , and the notion of length of a minimal connection connecting the topological singularities of . Stability results with respect to perturbations of the function are also presented.