On the Non-degeneracy of the Robin Function for the Fractional Laplacian on Symmetric Domains

In this work we prove, under symmetry and convexity assumptions on the domain \(\Omega \) $\mathrm{\Omega }$ , the non- degeneracy at zero of the Hessian matrix of the Robin function for the spectral fractional Laplacian. This work extends to the fractional setting the results of M. Grossi concerning the classical Laplace operator.