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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The Signorini problem for the heat equation: regul
arity of the solution and of the free boundary - G
arofalo\, N (Universit degli Studi di Padova)
DTSTART;TZID=Europe/London:20140416T151500
DTEND;TZID=Europe/London:20140416T161500
UID:TALK51959AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51959
DESCRIPTION:Over the past decade the lower-dimensional\, or Si
gnorini\, problem has received a great deal of att
ention\, especially after the 2004 breakthrough re
sult of Athanasopoulos and Caffarelli on the optim
al C^{1\,1/2} smoothness of the solution up to the
thin manifold. However\, until recently\, there h
as been no significant progress on the parabolic c
ounterpart of such optimal regularity and on the r
egularity of the free boundary. In this lecture I
will discuss recent joint work with D.Danielli\, A
. Petrosyan and T. To in which we give a comprehen
sive treatment of the parabolic Signorini problem
based on a generalization of Almgren's monotonicit
y of the frequency. This includes the proof of the
\noptimal regularity of solutions\, classification
of free boundary points\, the regularity of the r
egular set and the structure of the singular set.\
n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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