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SUMMARY:Nondegeneracy in the Obstacle Problem with a Degenerate Force Term
  - Yeressian Negarchi\, K (University of Zurich)
DTSTART:20140623T142000Z
DTEND:20140623T145000Z
UID:TALK53077@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk I present the proof of the optimal nondegeneracy 
 of the solution $u$ of the obstacle problem $	riangle u=fi_{{u>0}}$ in a 
 bounded domain $D ubsetmathbb{R}^{n}$\, where we only require $f$ to have 
 a nondegeneracy of the type $f(x)geqlambdaert (x_1\,ots\,x_p)ert^{lpha
 }$ for some $lambda>0$\, $1leq pleq n$ (an integer) and $lpha>0$. We prov
 e optimal uniform $(2+lpha)$-th order and nonuniform quadratic nondegener
 acy\, more precisely we prove that there exists $C>0$ (depending only on $
 n$\, $p$ and $lpha$) such that for $x$ a free boundary point and $r>0$ sm
 all enough we have $ up_{partial B_r(x)}ugeq Clambda (r^{2+lpha}+ert(x_1
 \,ots\,x_p)ert^{lpha}r^{2})$. I also present the proof of the optimal g
 rowth with the assumption $ert f(x)ertleqLambdaert (x_1\,ots\,x_p)ert
 ^{lpha}$ for some $Lambdageq 0$ and the porosity of the free boundary. \n
 \nPreprint: http://www.newton.ac.uk/preprints/NI14045.pdf\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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