Comptes Rendus
Partial Differential Equations
Fractional Laplacian: Pohozaev identity and nonexistence results
Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 505-508.

In this Note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semilinear problems with supercritical nonlinearities in star-shaped domains.

Dans cette Note, nous présentons lʼidentité de Pohozaev pour le Laplacien fractionnaire. Comme conséquence de cette identité, nous prouvons la non-existence de solutions non triviales pour les problèmes semi-linéaires avec nonlinéarité sur-critique dans des domaines étoilés.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.05.011

Xavier Ros-Oton 1; Joaquim Serra 1

1 Universitat Politècnica de Catalunya, Departament Matemàtica Aplicada I, Avda. Diagonal 647, 08028 Barcelona, Spain
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Xavier Ros-Oton; Joaquim Serra. Fractional Laplacian: Pohozaev identity and nonexistence results. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 505-508. doi : 10.1016/j.crma.2012.05.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.05.011/

[1] M.M. Fall; T. Weth Nonexistence results for a class of fractional elliptic boundary value problems | arXiv

[2] S.I. Pohozaev On the eigenfunctions of the equation Δu+λf(u)=0, Dokl. Akad. Nauk SSSR, Volume 165 (1965), pp. 1408-1411

[3] X. Ros-Oton, J. Serra, The Pohozaev identity for the fractional Laplacian, forthcoming.

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