Regularity of Minimizers of Shape Optimization Problems involving Perimeter

Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the moving

On the contrary, if the limit value exists but the uniform value does not, he really needs to know the time horizon before choosing a control.. We will prove that our results do

However, for shape optimization of the type considered here, the situation is slightly better and, as proved in [5],[4], positivity does imply existence of a strict local minimum

This permits to infer the necessary regularity on the solutions u ε of the regularized problem, in order to justify the manipulations needed to obtain a priori Lipschitz

Our main objective is to obtain qualitative properties of optimal shapes by exploiting first and second order optimality conditions on (1) where the convexity constraint is

Dual parametrization: Since our results are stated for the analytic functionals (4), we may apply them to the dual parametrization of convex sets instead of the parametrization with

Relaxed formulation for the Steklov eigenvalues: existence of optimal shapes In this section we extend the notion of the Steklov eigenvalues to arbitrary sets of finite perime- ter,

First, we mention that the numerical results satisfy the theoretical properties proved in [9] and in Theorem 1.3: the lack of triple points, the lack of triple points on the