Institut de Mathématiques de Marseille, UMR 7373




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17 septembre 2019: 2 événements

Séminaire

  • Agenda ERC IChaos

    Du 12 au 28 septembre - A.BUFETOV

    Scientific collaboration with Marco Bertola (SISSA Trieste)

    Résumé : + external member of Commitee PhD Ruzza

    Lieu : SISSA - Trieste, Italy

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  • Séminaire Analyse Appliquée (AA)

    Mardi 17 septembre 11:00-12:00 - Ariel SALORT - Universidad de Buenos Aires

    A limiting obstacle problem for the inhomogeneous p-fractional Laplacian

    Résumé : In this manuscript we study an inhomogeneous obstacle type problem involving a fractional p-Laplacian type operator. First, we focus our attention in establishing existence and uniform estimates for any family of solutions u pp≥2 which depend on the data of the problem and universal parameters. Next, we analyze the asymptotic behavior of such a family as p → ∞. At this point, we prove that limp→∞ u p(x) = u∞(x) there exists (up to a subsequence), verifies a limiting obstacle type problem in the viscosity sense, and it is an s-Hölder continuous function. We also present several explicit examples, as well as further features of the limit solutions and their free boundaries. In order to establish our results we overcome several technical difficulties and develop new strategies, which were not present in the literature for this type of problems. Finally, we remark that our results are new even for problems governed by fractional p-Laplacian operator, as well as they extend the previous ones by dealing with more general non-local operators, source terms and boundary data.
    The manuscript is available on https://link.springer.com/content/pdf/10.1007%2Fs00526-019-1573-5.pdf

    JPEG - 8.2 ko
    Ariel SALORT

    Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
    39 rue Frédéric Joliot-Curie
    13453 MARSEILLE cedex 13

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