Optimal design problems with fractional diffusions

الأصل · EN

In this article we study optimization problems ruled by α-fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of class C⁰,α (optimal regularity), and that the free boundary is a C¹,γ surface, up to a Hⁿ⁻¹-negligible set.