# Shape optimization problems for graphs

## Berardo Ruffini (Institut Montpelliérain Alexander Grothendieck, Université de Montpellier)

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

Abstract.

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.

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