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UID:3053@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190917T110000
DTEND;TZID=Europe/Paris:20190917T120000
DTSTAMP:20190902T090000Z
URL:https://www.i2m.univ-amu.fr/evenements/a-limiting-obstacle-problem-for
 -the-inhomogeneous-p-fractional-laplacian/
SUMMARY: (...): A limiting obstacle problem for the inhomogeneous p-fractio
 nal Laplacian
DESCRIPTION:: In this manuscript we study an inhomogeneous obstacle type pr
 oblem involving a fractional p-Laplacian type operator. First\, we focus o
 ur attention in establishing existence and uniform estimates for any famil
 y of solutions {u p}p≥2 which depend on the data of the problem and univ
 ersal parameters. Next\, we analyze the asymptotic behavior of such a fami
 ly 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 pr
 oblem in the viscosity sense\, and it is an s-Hölder continuous function.
  We also present several explicit examples\, as well as further features o
 f the limit solutions and their free boundaries. In order to establish our
  results we overcome several technical difficulties and develop new strate
 gies\, which were not present in the literature for this type of problems.
  Finally\, we remark that our results are new even for problems governed b
 y fractional p-Laplacian operator\, as well as they extend the previous on
 es by dealing with more general non-local operators\, source terms and bou
 ndary data. The manuscript is available on  https://link.springer.com/cont
 ent/pdf/10.1007%2Fs00526-019-1573-5.pdf  http://mate.dm.uba.ar/~asalort/
CATEGORIES:Séminaire,Analyse Appliquée
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DTSTART:20190331T030000
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