Some remarks about a notion of rearrangement
Un risultato di convergenza variazionale per funzionali di tipo Ginzburg-Landau in dimensione qualunque
We describe an approach via -convergence to the asymptotic behaviour of (minimizers of) complex Ginzburg-Landau functionals in any space dimension, summarizing the results of a joint research with S. Baldo and C. Orlandi [ABO1-2].
Local Mappings on spaces of differentiable functions.
Errata to: Local Mappings on Spaces of Differentiable Functions [1].
A uniqueness result for the continuity equation in two dimensions
We characterize the autonomous, divergence-free vector fields on the plane such that the Cauchy problem for the continuity equation admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential associated to . As a corollary we obtain uniqueness under the assumption that the curl of is a measure. This result can be extended to certain non-autonomous vector fields with bounded divergence....
Functions with prescribed singularities
The distributional -dimensional Jacobian of a map in the Sobolev space which takes values in the sphere can be viewed as the boundary of a rectifiable current of codimension carried by (part of) the singularity of which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary of codimension can be realized as Jacobian of a Sobolev map valued in . In case is polyhedral, the map we construct...
À propos de certains problèmes inverses hybrides
Dans cet exposé, nous présentons quelques résultats récents concernant certains problèmes d’identification de paramètres de type hybride, aussi appelés multi-physiques, pour lesquels le modèles physique sous-jacent est une équation aux dérivées partielles elliptique.
Gap phenomenon for some autonomous functionals.
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