On fractional Laplacians – 3

Musina, Roberta; Nazarov, Alexander I.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 832-841.

We investigate the role of the noncompact group of dilations in $R^n$ 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.

Classification : 47A63, 35A23
Mots clés : Fractional Laplace operators, Navier and Dirichlet boundary conditions, Sobolev inequality, critical dimensions

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