Convergence et relaxation de fonctionnelles du calcul des variations à croissance linéaire. Application à l'homogénéisation en plasticité
Relaxation for a class of nonconvex functionals defined on measures
Homogenization of elliptic problems in a fiber reinforced structure. Non local effects
Characterization of optimal shapes and masses through Monge-Kantorovich equation
We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.
Relaxation results for some free discontinuity problems.
Mean curvature of a measure and related variational problems
Integral representation and relaxation of convex local functionals on
On the curvature and torsion effects in one dimensional waveguides
We consider the Laplace operator in a thin tube of with a Dirichlet condition on its boundary. We study asymptotically the spectrum of such an operator as the thickness of the tube's cross section goes to zero. In particular we analyse how the energy levels depend simultaneously on the curvature of the tube's central axis and on the rotation of the cross section with respect to the Frenet frame. The main argument is a -convergence theorem for a suitable sequence of quadratic energies.
BV functions with respect to a measure and relaxation of metric integral functionals.
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