Chiara Bianchini

A SHARP ROGERS AND SHEPHARD INEQUALITY FOR THE p-DIFFERENCE BODY OF PLANAR CONVEX BODIES

We prove a sharp Rogers and Shephard type inequality for the p-difference body of a convex body in the two-dimensional case, for every p ≥ 1.

Elastic energy of a convex body

In this paper a Blaschke-Santaló diagram involving the area, the perimeter and the elastic energy of planar convex bodies is considered. More precisely we give a description of set

An overdetermined problem with non-constant boundary condition

We investigate an overdetermined Torsion problem, with a non-constant positively homogeneous boundary constraint on the gradient. We interpret this problem as the Euler equation of a shape optimization problems, we prove existence and regularity of a solution. Moreover several geometric properties of the solution are shown.

A Bernoulli problem with non-constant gradient boundary constraint

In this article, we present a result about the existence and convexity of solutions to a free boundary problem of Bernoulli type, with non-constant gradient boundary constraint depending on the outer unit normal. In particular, we prove that, in the convex case, the existence of a subsolution guarantees the existence of a classical solution, which is proved to be convex.

A Note on an Overdetermined Problem for the Capacitary Potential

We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.