OPTIFORM

This project is devoted to theoretical and numerical analysis of modern shape optimization problems. It gathers leading experts located in the Universities of Nancy, Rennes, Grenoble and Paris-Dauphine. For the theoretical point of view, the main scientific challenge is the qualitative study of optimal shapes for some classes of shape functional involving partial differential equations and/or geometric quantities associated naturally with shapes: measure, perimeter, curvature. We are particularly interested to handle non-smooth and singular shapes to understand the minimal regularity under which one can extract information from the optimality conditions, to prove this regularity to obtain qualitative information about the optimal shape and to compute them. Precisely, in our project we will concentrate on the following topics: Spectral problems, Critical shapes and optimality conditions, Inverse problems in Fluids, Optimal shapes with convexity constraints, Computation of optimal shapes. We also want to develop the “SHAPEBOX” which is a web-tool for solving model shape optimization problems.