dc.contributor.author Coville, Jérôme dc.date.accessioned 2014-06-02T08:25:36Z dc.date.available 2014-06-02T08:25:36Z dc.date.issued 2007 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/13394 dc.language.iso en en dc.subject Nonlocal diffusion operators en dc.subject maximum principles en dc.subject sliding methods en dc.subject.ddc 515 en dc.title Maximum principles, sliding techniques and applications to nonlocal equations en dc.type Article accepté pour publication ou publié dc.description.abstracten This paper is devoted to the study of maximum principles holding for some nonlocal diffusion operators defined in (half-) bounded domains and its applications to obtain qualitative behaviors of solutions of some nonlinear problems. It is shown that, as in the classical case, the nonlocal diffusion considered satisfies a weak and a strong maximum principle. Uniqueness and monotonicity of solutions of nonlinear equations are therefore expected as in the classical case. It is first presented a simple proof of this qualitative behavior and the weak/strong maximum principle. An optimal condition to have a strong maximum for operator $\mathcal{M}[u] :=J\star u -u$ is also obtained. The proofs of the uniqueness and monotonicity essentially rely on the sliding method and the strong maximum principle. en dc.relation.isversionofjnlname Electronic Journal of Differential Equations dc.relation.isversionofjnlissue 68 en dc.relation.isversionofjnldate 2007 dc.relation.isversionofjnlpages 1-23 en dc.relation.isversionofjnlpublisher EJDE en dc.subject.ddclabel Analyse en dc.relation.forthcoming non en dc.relation.forthcomingprint non en
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