My curent work

My work is about shape optimization, it is about solving problems of the form

where \(\mathcal{A} \subset \mathcal{P}(\mathbf{R}^d)\) represents the class of admissible shapes, typically open subsets of \(\mathbf{R}^d\) with given volume or subsets of a box \(D\subset\mathbf{R}^d\) and \(F\) is a given functional.

In my work, depending on the context, I’m lead to use both a theoretical and a numerical approach that complement each other.