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dc.contributor | Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions |
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dc.contributor.author | Ros Oton, Xavier |
dc.contributor.author | Serra Montolí, Joaquim |
dc.date | 2015-01-02 |
dc.identifier.citation | 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. |
dc.identifier.citation | 0360-5302 |
dc.identifier.citation | 10.1080/03605302.2014.918144 |
dc.identifier.uri | http://hdl.handle.net/2117/84612 |
dc.description.abstract | 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. |
dc.description.abstract | Peer Reviewed |
dc.language.iso | eng |
dc.relation | http://www.tandfonline.com/doi/abs/10.1080/03605302.2014.918144?journalCode=lpde20#.VPWE5-G2r0w |
dc.rights | info:eu-repo/semantics/openAccess |
dc.subject | 35J60 |
dc.subject | 45K05 |
dc.subject | Nonexistence |
dc.subject | Integro-differential operators |
dc.subject | Supercritical nonlinearities |
dc.subject | Fractional Laplacian |
dc.subject | FRACTIONAL LAPLACIAN |
dc.subject | ELLIPTIC-EQUATIONS |
dc.subject | POHOZAEV IDENTITY |
dc.subject | OPERATORS |
dc.subject | INEQUALITIES |
dc.subject | BOUNDARY |
dc.subject | 35J60 |
dc.subject | 45K05 |
dc.title | Nonexistence results for nonlocal equations with critical and supercritical nonlinearities |
dc.type | info:eu-repo/semantics/submittedVersion |
dc.type | info:eu-repo/semantics/article |