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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The Signorini problem\, fractional Laplacians and
the language of semigroups - Stinga\, PR (Universi
ty of Texas at Austin)
DTSTART;TZID=Europe/London:20140624T113000
DTEND;TZID=Europe/London:20140624T120000
UID:TALK53126AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53126
DESCRIPTION:The Signorini problem can be equivalently formulat
ed as a thin obstacle problem for an elastic membr
ane. The resulting free boundary problem turns out
to be equivalent to the obstacle problem for the
fractional Laplacian on the whole space. We will s
how how to understand this problem under the light
of the language of semigroups that I developed in
my PhD thesis (2010). In particular\, we are able
to consider different kinds of Signorini problems
that are equivalent to obstacle problems for frac
tional powers of operators different than the Lapl
acian on the whole space. Boundary conditions of d
ifferent kinds (Dirichlet\, Neumann\, periodic) an
d radial solutions can also be treated with this u
nified language. Another advantage is that this la
nguage avoids the use of the Fourier transform. Th
e basic regularity results (Harnack inequalities\,
Schauder estimates) for these fractional nonlocal
operators can be studied by means of the generali
zation of the Caffarelli--Silvestre extensio n pro
blem that I proved in my PhD thesis. It turns out
that the solution for the extension problem can be
written in terms of the heat semigroup.\n\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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