On fractional Laplacians -- 3

We investigate the role of the noncompact group of dilations in ${\mathbb{R}}^n$ on the difference of the quadratic forms associated to the fractional Dirichlet and Navier Laplacians. Then we apply our results to study the Brezis–Nirenberg effect in two families of noncompact boundary value problems involving the Navier-Laplacian.