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.
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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@article{CRMATH_2012__350_9-10_505_0, author = {Ros-Oton, Xavier and Serra, Joaquim}, title = {Fractional {Laplacian:} {Pohozaev} identity and nonexistence results}, journal = {Comptes Rendus. Math\'ematique}, pages = {505--508}, publisher = {Elsevier}, volume = {350}, number = {9-10}, year = {2012}, doi = {10.1016/j.crma.2012.05.011}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.05.011/} }
TY - JOUR AU - Ros-Oton, Xavier AU - Serra, Joaquim TI - Fractional Laplacian: Pohozaev identity and nonexistence results JO - Comptes Rendus. Mathématique PY - 2012 SP - 505 EP - 508 VL - 350 IS - 9-10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.05.011/ DO - 10.1016/j.crma.2012.05.011 LA - en ID - CRMATH_2012__350_9-10_505_0 ER -
%0 Journal Article %A Ros-Oton, Xavier %A Serra, Joaquim %T Fractional Laplacian: Pohozaev identity and nonexistence results %J Comptes Rendus. Mathématique %D 2012 %P 505-508 %V 350 %N 9-10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.05.011/ %R 10.1016/j.crma.2012.05.011 %G en %F CRMATH_2012__350_9-10_505_0
Ros-Oton, Xavier; Serra, Joaquim. Fractional Laplacian: Pohozaev identity and nonexistence results. Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 505-508. doi : 10.1016/j.crma.2012.05.011. http://archive.numdam.org/articles/10.1016/j.crma.2012.05.011/
[1] Nonexistence results for a class of fractional elliptic boundary value problems | arXiv
[2] On the eigenfunctions of the equation , 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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