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On the approximation of the elastica functional in radial symmetry
Full text linkWe prove a result concerning the approximation of the elastica functional with a sequence of second order functionals, under radial symmetry assumptions. This theorem is strictly related to a conjecture of De Giorgi [8].
Received: 26 July 2004, Accepted: 19 October 2004, Published online: 22 December 2004
The first author is grateful to Maurizio Paolini for useful discussions.
The second author gratefully acknowledges the hospitality and the support of the Max Planck Institute for Gravitational Physics in Golm, where this paper was completed
A varifolds representation of the relaxed elastica functional
No full textWe prove a new representation result for the L1-lower semicontinuous envelope of the elastica functional in terms of a minimum problem over a suitable class of varifolds. We also show a representation result in a suitable class of Sobolev-type submanifolds
Some aspects of the variational nature of mean curvature flow
No full textWe show that the classical solution of the heat equation can be seen as the minimizer of a suitable functional defined in space-time. Using similar ideas, we introduce a functional F on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related with F. We show some connections between minimizers of F and mean curvature flow
Anisotropic geometric functionals and gradient flows
Full text linkWe survey some recent results on the gradient flow of an anisotropic surface en-ergy, the integrand of which is one-homogeneous in the normal vector. We discuss the reasonsfor assuming convexity of the anisotropy, and we review some known results in the smooth,mixed and crystalline case. In particular, we recall the notion of calibrability and the relatedfacet-breaking phenomenon. Minimal barriers as weak solutions to the gradient flow in case ofnonsmooth anisotropies are proposed. Furthermore, we discuss some relations between cylin-drical anisotropies, the prescribed curvature problem and the capillarity problem. We concludethe paper by examining some higher order geometric functionals. In particular we discuss theanisotropic Willmore functional and compute its first variation in the smooth case
Characterization and representation of the lower semicontinuous envelope of the elastica functional
No full textWe 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
Response of explants and cultured cells of oleander to inoculation with strains of Pseudomonas syringae subsp. savastanoi
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