SEMINARI DI CALCOLO DELLE VARIAZIONI
Abstract. Consider the problem of transporting some objects
between N distinct locations. Depending on how we package
together different objects and on how the transport cost (per
unit of distance traveled) depends on the package that we are
moving, we may cook up a minimum-cost transport strategy.
Is it always the best option to let our objects travel independently
of each other, or is it sometimes more cost-efficient to merge/split
packages along the way, following a branched, tree-like, global
Abstract. We show that the classical results about rotating
a line segment in arbitrarily small area, and the existence
of a Besicovitch and a Nikodym set hold if we replace the
line segment by an arbitrary rectifiable set.
This is joint work with Marianna Csörnyei.
Abstract. In the 1930s Sadowsky derived an asymptotic theory for narrow ribbons. We here provide a rigorous derivation of the generalized Sadowsky theory starting from nonlinear three-dimensional elasticity by means of Γ-convergence. On a technical level, this involves capturing a contribution to the asymptotic energy functional generated by a nonlinear constraint which is satisfied only approximately. It also involves the construction of fine-scale ‘corrugations’ capable of reaching a bending energy regime that is strictly below that of the original Sadowsky functional.
Abstract. We show some recent results on convex sets in Wiener spaces. We characterize the essential and reduced boundary of open convex sets and investigate integration by parts formulae. Of particular interest is the investigation of trace theorems for functions of bouned variation on boundaries of subsets in Wiener spaces.
We study a functional in which perimeter and regularized dipolar repulsion compete under a volume constraint.
In contrast to previously studied similar problems, the nonlocal term contributes to the perimeter term to leading order for small regularization parameters.