Analyse géométrique des formes optimales – GAOS

The main scientific challenge is the qualitative study of optimal shapes for some classes of shape functionals 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 (with or without constraints), to understand the minimal regularity under which one can extract information from the optimality conditions, to prove this regularity and finally to obtain qualitative information about the optimal shape. Understating these points is crucial for developing new efficient numerical methods to approximate optimal shapes.