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SUMMARY:Optimality and stability of the radial shapes for the Sobolev trac
 e constant - Simone Cito (Università del Salento)
DTSTART:20260205T121500Z
DTEND:20260205T124500Z
UID:TALK239836@talks.cam.ac.uk
DESCRIPTION:In this work we establish the optimality and the stability of 
 the ball for the Sobolev trace operator $W^{1\,p}(\\Omega)\\hookrightarrow
  L^q(\\partial\\Omega)$ among convex sets of prescribed perimeter for any 
 $1< p <+\\infty$ and $1\\le q\\le p$. More precisely\, we prove that the t
 race constant $\\sigma_{p\,q}$ is maximal for the ball and the deficit is 
 estimated from below by the Hausdorff asymmetry. With similar arguments\, 
 we prove the optimality and the stability of the spherical shell for the S
 obolev exterior trace operator $W^{1\,p}(\\Omega_0\\setminus\\overline{\\T
 heta})\\hookrightarrow L^q(\\partial\\Omega_0)$ among open sets obtained r
 emoving from a convex set $\\Omega_0$ a suitably smooth open hole $\\Theta
 \\subset\\subset\\Omega_0$\, with $\\Omega_0\\setminus\\overline{\\Theta}$
  satisfying a volume and an outer perimeter constraint.
LOCATION:Seminar Room 1\, Newton Institute
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