Calculus of Variations and Geometric Measure Theory

Shape optimization problems for graphs

Berardo Ruffini (Università di Bologna)

created by magnani on 11 May 2012
modified by ruffini on 24 Jun 2012

23 may 2012 -- 17:00   [open in google calendar]

Sala Seminari, Department of Mathematics, Pisa University


In this seminar we will discuss a shape optimization problem of the form \[ \min\big\{J(\Gamma)\ :\ \Gamma\in\mathcal{A},\ \mathcal{H}^1(\Gamma)=l\ \big\}, \] where $\mathcal{A}$ is a suitable set of graphs immersed in $\mathbb R^d$ with set of vertices $E(\Gamma)$ containing some prescribed set of points $\mathcal{D}=\{D_1,\dots,D_k\}$, and $J$ depends on $\Gamma$ via some differential operator on $\Gamma$ (for example, the Dirichlet Laplacian). We will analyze the existence of a solution in the class $\mathcal{A}$ and show some techniques useful to obtain explicit examples. Joint work with Giuseppe Buttazzo and Bozhidar Velichkov.