On Shape Optimization Theory with Fractional Laplacian

The fractional Laplacian is a nonlocal operator that appears in biology, in physic, in fluids dynamic, in financial mathematics and probability. This paper deals with shape optimization problem associated to the fractional laplacian ∆s, 0 under constraints volume. Finally, shape derivative of the functional is established by using Hadamard formula’s and an optimality condition is also given.