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UID:6002@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190917T110000
DTEND;TZID=Europe/Paris:20190917T120000
DTSTAMP:20190902T090000Z
URL:https://www.i2m.univ-amu.fr/events/a-limiting-obstacle-problem-for-the
-inhomogeneous-p-fractional-laplacian/
SUMMARY:A limiting obstacle problem for the inhomogeneous p-fractional Lapl
acian -
DESCRIPTION:In this manuscript we study an inhomogeneous obstacle type prob
lem involving a fractional p-Laplacian type operator. First\, we focus our
attention in establishing existence and uniform estimates for any family
of solutions {u p}p≥2 which depend on the data of the problem and univer
sal 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) t
here exists (up to a subsequence)\, verifies a limiting obstacle type prob
lem in the viscosity sense\, and it is an s-Hölder continuous function. W
e also present several explicit examples\, as well as further features of
the limit solutions and their free boundaries. In order to establish our r
esults we overcome several technical difficulties and develop new strategi
es\, which were not present in the literature for this type of problems. F
inally\, 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 bound
ary data. The manuscript is available on https://link.springer.com/conten
t/pdf/10.1007%2Fs00526-019-1573-5.pdf http://mate.dm.uba.ar/~asalort/
CATEGORIES:Séminaire Analyse Appliquée (AA)
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DTSTART:20190331T030000
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