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.
Characterization and representation of the lower semicontinuous envelope of the elastica functional
Bellettini, Giovanni;
2004-01-01
Abstract
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.File in questo prodotto:
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