Characterization and representation of the lower semicontinuous envelope of the elastica functional

We characterize the lower semicontinuous envelope (F) over bar of the functional F(E) := integral(partial derivativeE)[1 + \kappa(partial derivativeE)\(p)]dH(1), defined on boundaries of sets E subset of R-2, where kappa(partial derivativeE) denotes the curvature of partial derivativeE and p > 1. Through a desingularization procedure, we find the domain of (F) over bar and its expression, by means of different representation formulas. (C) 2004 Elsevier SAS. All fights reserved