On fractional Laplacians – 3

On fractional Laplacians – 3

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...

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Veröffentlicht in:ESAIM. Control, optimisation and calculus of variations optimisation and calculus of variations, 2016-07, Vol.22 (3), p.832-841
Hauptverfasser: Musina, Roberta, Nazarov, Alexander I.
Format: Artikel
Sprache:eng
Schlagworte:
35A23
47A63
Boundary value problems
critical dimensions
Dirichlet problem
Fluid flow
Fractional Laplace operators
Navier and Dirichlet boundary conditions
Quadratic forms
Sobolev inequality
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Zusammenfassung: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.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2015032