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UID:news493@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181229T225814
DTSTART;TZID=Europe/Zurich:20131204T151500
SUMMARY:Seminar Analysis: Xavier Ros-Oton (Polytechnic University of Catalo
 nia)
DESCRIPTION:We study the boundary regularity of solutions to elliptic  inte
 gro-differential equations. First we prove that\, for the fractional  Lapl
 acian (-Δ)s with s∈(0\,1)\, solutions u satisfy that u/ds is Hölder co
 ntinuous up to the boundary\, where d(x) is the  distance to the boundary 
 of the domain Ω. We will show that\, in  this fractional context\, the qu
 antity u/ds|∂Ω plays  the role that the normal derivative plays in seco
 nd order equations.  Finally\, we also present new boundary regularity res
 ults for fully  nonlinear integro-differential equations.
X-ALT-DESC: \nWe study the boundary regularity of solutions to elliptic  in
 tegro-differential equations. First we prove that\, for the fractional  La
 placian (-Δ)<sup>s</sup> with s∈(0\,1)\, solutions u satisfy that u/d<s
 up>s</sup> is Hölder continuous up to the boundary\, where d(x) is the  d
 istance to the boundary of the domain Ω. We will show that\, in  this fra
 ctional context\, the quantity u/d<sup>s</sup>|<sub>∂Ω</sub> plays  the
  role that the normal derivative plays in second order equations.  Finally
 \, we also present new boundary regularity results for fully  nonlinear in
 tegro-differential equations.
DTEND;TZID=Europe/Zurich:20131204T161500
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