On fractional Laplacians – 3

Musina, Roberta; Nazarov, Alexander I.

doi:10.1051/cocv/2015032

Musina, Roberta ¹ ; Nazarov, Alexander I.^2,³

¹ Dipartimento di Matematica ed Informatica, Università di Udine, via delle Scienze, 206 – 33100 Udine, Italy
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.

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

Résumé

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.

Reçu le : 2015-03-27

MR Zbl

DOI : 10.1051/cocv/2015032

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

Affiliations des auteurs :

Musina, Roberta ¹ ; Nazarov, Alexander I. ^{2, 3}

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Musina, Roberta; Nazarov, Alexander I. On fractional Laplacians – 3. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 832-841. doi : 10.1051/cocv/2015032. https://www.numdam.org/articles/10.1051/cocv/2015032/

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