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oai:recercat.cat:2117/846122026-01-21T05:58:51Zcom_2072_1033col_2072_452950

Nonexistence results for nonlocal equations with critical and supercritical nonlinearities Ros Oton, Xavier Serra Montolí, Joaquim Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions 35J60 45K05 Nonexistence Integro-differential operators Supercritical nonlinearities Fractional Laplacian FRACTIONAL LAPLACIAN ELLIPTIC-EQUATIONS POHOZAEV IDENTITY OPERATORS INEQUALITIES BOUNDARY 35J60 45K05 We prove nonexistence of nontrivial bounded solutions to some nonlinear problems involving nonlocal operators of the form; [GRAPHICS]; These operators are infinitesimal generators of symmetric Levy processes. Our results apply to even kernels K satisfying that K(y)|y|( n+sigma) is nondecreasing along rays from the origin, for some sigma is an element of (0, 2) in case a ( ij ) equivalent to 0 and for sigma = 2 in case that (a ( ij )) is a positive definite symmetric matrix.; Our nonexistence results concern Dirichlet problems for L in star-shaped domains with critical and supercritical nonlinearities (where the criticality condition is in relation to n and sigma).; We also establish nonexistence of bounded solutions to semilinear equations involving other nonlocal operators such as the higher order fractional Laplacian (- Delta)( s ) (here s > 1) or the fractional p-Laplacian. All these nonexistence results follow from a general variational inequality in the spirit of a classical identity by Pucci and Serrin. Peer Reviewed Postprint (author's final draft) 2015-01-02 Article Ros, X., Serra, J. Nonexistence results for nonlocal equations with critical and supercritical nonlinearities. "Communications in partial differential equations", 02 Gener 2015, vol. 40, núm. 1, p. 115-133. 0360-5302 https://hdl.handle.net/2117/84612 10.1080/03605302.2014.918144 eng http://www.tandfonline.com/doi/abs/10.1080/03605302.2014.918144?journalCode=lpde20#.VPWE5-G2r0w Open Access 19 p. application/pdf