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SUMMARY:The Signorini problem for the heat equation: regularity of the sol
 ution and of the free boundary - Garofalo\, N (Universit degli Studi di Pa
 dova)
DTSTART:20140416T141500Z
DTEND:20140416T151500Z
UID:TALK51959@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Over the past decade the lower-dimensional\, or Signorini\, pr
 oblem has received a great deal of attention\, especially after the 2004 b
 reakthrough result of Athanasopoulos and Caffarelli on the optimal C^{1\,1
 /2} smoothness of the solution up to the thin manifold. However\, until re
 cently\, there has been no significant progress on the parabolic counterpa
 rt of such optimal regularity and on the regularity of the free boundary. 
 In this lecture I will discuss recent joint work with D.Danielli\, A. Petr
 osyan and T. To in which we give a comprehensive treatment of the paraboli
 c Signorini problem based on a generalization of Almgren's monotonicity of
  the frequency. This includes the proof of the\noptimal regularity of solu
 tions\, classification of free boundary points\, the regularity of the reg
 ular set and the structure of the singular set.\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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