On fractional Laplacians – 3
1 Dipartimento di Matematica ed
Informatica, Università di Udine, via delle Scienze, 206 –
2 St.Petersburg Department of Steklov Institute, Fontanka 27, St.Petersburg, 191023, Russia.
3 St.Petersburg State University, Universitetskii pr. 28, St.Petersburg, 198504, Russia.
Received: 27 March 2015
We investigate the role of the noncompact group of dilations in Rn 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.
Mathematics Subject Classification: 47A63 / 35A23
Key words: Fractional Laplace operators / Navier and Dirichlet boundary conditions / Sobolev inequality / critical dimensions
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