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Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 505-508 (mai 2012)
Doi : 10.1016/j.crma.2012.05.011
Received : 3 May 2012 ;  accepted : 25 May 2012
Fractional Laplacian: Pohozaev identity and nonexistence results
Laplacien fractionnaire : identité de Pohozaev et résultats de nonexistence

Xavier Ros-Oton , Joaquim Serra
Universitat Politècnica de Catalunya, Departament Matemàtica Aplicada I, Avda. Diagonal 647, 08028 Barcelona, Spain 


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.

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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.

The full text of this article is available in PDF format.

© 2012  Published by Elsevier Masson SAS de la part de Académie des sciences.
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