Dominik Stantejsky (Institut Elie Cartan de Lorraine) : On the shape optimisation of the first solenoidal Maxwell eigenvalue

In this talk, I will present a recent result on the minimisation of the first solenoidal Maxwell eigenvalue  λ^max₁(Ω) in perfectly conducting cavities under perimeter constraint. While this problem is known to be ill-posed, one can prove that λ^max₁(Ω) has a positive infimum in the class of bounded convex cavities. Whether an optimal domain exists remains an open question, but I will discuss several negative results that provide obstructions to its existence.